They weren't. The Duchy of Courland and Semigallia, which was a vassal of the Polish-Lithuanian Commonwealth in modern day Latvia, had a colony in Tobago in the West Indies. Sweden had a colony in Delaware. Russia had colonies on the west coast in Alaska and at Fort Ross in Northern California.
There are a number of reasons that could be attributed to it all the way down to the mentality and traditions of each nation in question, but I think the biggest two are distance and availability of resources.
The initial drive which lead to the 'discovery' of the new world was to open up trade routes to India and China. India and China did not need to find these trade routes because the people and their money were already knocking down doors to get to them. The impetus was on the Europeans to find more efficient routes and bypass middlemen. Colonialism is almost always based on economics, and colonies were usually designed to extract resources from their location, not to spread a population. Population spreading and growth was just a side effect of a successful colony. Colonies rarely made a particular country that much richer but they did make some people who lived in that country richer.
The other is distance and practicality. Crossing the Atlantic is much easier due to distance and trade winds. To take the trade winds of the Pacific would push you up along the frigid coast of the Kamchatka peninsula, across the Aleutian Islands of Alaska, and down the western coast of north America. Going back was perilous as well as you had to cross the vastness of the equatorial region of the Pacific where there are almost no islands for 5,000 miles.
Atlantic Trade winds were very helpful in this respect. They would take you south from Europe to Cape Verde off the African Coast, and then straight across to the Caribbean, a mere 2,800 mile journey. I don't mean to make it sound that easy, but compared to a Pacific journey it would be. From there it was just a matter of island hopping to the rest of the continents.
All that said, countries outside western Europe were interested in colonization and colonialism, just not in the New World due to practicality. The Empire of Japan certainly had colonial ambitions, as did Italian states. Russia even colonized all the way to the Pacific ocean.
Western Europe had the easiest access to the New World because of of its proximity to the Atlantic Ocean. I'm sure other countries were interested in exploring and colonizing the New World, but geography blocked them from establishing colonies and keeping them supplied and defended, because foreign, potentially hostile nations stood between them and the Atlantic.
Woof, talk about a big and non specific question.
Here are a few key points to consider:
State centralization had gone furthest in the parts of western Europe facing the Atlantic for whatever reason.
Most of the best early staging points for the principal colonial routes were controlled by countries on the north Atlantic
Domestic and foreign policy troubles distracted potential competition from other states with an interest in Atlantic seafaring, such as Venice, Genoa and the Hanseatic states
Using Venice in particular as the obvious potential colonial power -- being as they had long established colonies in Crete, Constantinople, Cyprus, Acre and other parts of the Mediterranean and Black Sea -- they were tied up in fighting in the Italian Wars and against the Ottoman Empire, plus had poor relations with the Portuguese (according to Norwich) plus were focused on traditional (and far more lucrative) trade through Alexandria
Power projection across the Atlantic required a greater population and capital investment than most states were capable of given their existing foreign policy commitments.
It wasn't until pretty late in the game that the route around Africa became cheaper than the route through Alexandria, partly because the Mamelukes (and later the Turks) cut rates on through traffic to keep it competitive
Navigational maps (rutters) that included information about currents, prevailing winds, reefs, location of lands and sailing directions were carefully guarded and difficult to acquire, complicating the planning of a colonial excursion
Now I am far from an expert in the subject but one must consider that there is a difference in a country being interested in colonialism and actually building a colonial empire. Some nations may have been interested in such colonialism but may have never we carried it out.
Some countries in Eastern Europe such as Courland and Brandenburg-Prussia(one could debate if that is eastern or western), did have colonies in Africa and the Carribean.
My apologies for the lack of value of this comment, but hopefully it provides some food for thought for the discussion from Historians here as I am quite excited to read on this.
I cannot tell you why were they the only countries interested in it, or even if that sentence is true, what I can tell you is the reason for one of those countries being so interested in it. Portugal
Let's look a bit at it's history before that country started the Age of Discovery.
Portugal as you may know is a very small country bordered on the North and East by Spain (then Castille), and on the West and South by the Atlantic Ocean. It's land area represent's about 15% of the Iberian Peninsula, has a different and more unified feudalism than the rest of Europe and due to those factors, small size, small strength compared to it's bigger neighbour, and unity, Portugal had no reason whatsoever to become engaged in politics and disputed with the rest of the Continent. It's to no surprise that many Spanish monarchs considered it to be a geographic aberration.
In 1385 Portugal emerges from a two year succession crisis victorious against Castille, and the new King is D. João I, he has plenty of children one of them becomes of great importance to the start of the Discovery age - D. Henrique or in english Prince Henry - The Navigator.
He became the rich governor of the order of christ, and sponsored a "school of navigation" where knowledge and techniques would be brought to be learned from and perfected, and a large number of expeditions to map the coast of Africa, not just for the sake of it, but for two reasons linked to eachother. To see the extent of the Muslim territory in Africa, and spread Christianity. Every pit stop the ships took the captains would order the sailors to erect a cross, with the country's arms, they would celebrate a mass.
When speaking about Colonization and Discovery, and in this particular Portuguese case, spreading christianity and amass wealth were given almost the same importance. Portugal had a a small population, so colonies were far from portuguese horizons, in the late 14th and through the 15th century, Portugal developed a trade empire and in some cases a monopoly (dominated atlantic slave trading for almost 100 years)
And keeping on to trade (I will get to colonization soon). In 1498 Vasco da Gama, sailed past the southern tip of africa in to the Indian ocean and reached India. On a side note, I saw a reply to this thread that said traditional trade through alexandria, so I assume silk road or close to it, was far more lucrative) Vasco da Gama expedition to india with 3 ships, brought back six times it's cost in spices. And then it began what could be called a trading post empire, with the portuguese charging tarifs to all trade in the Indian Ocean. This was mostly done by force at first and later through strategic aliances, although vastly outnumbered, better ships and much better naval artillery were no match for the vessels and fortresses of the nations that priveously dominated the indian ocean trade (I should mention now that I mostly refer to the coasts of the arabian sea until Sri-lanka). The Indian Ocean became for a while the Portugese "Mare Clausum"
Now Colonization. In 1500 Portugal discovers the coast of Brazil, and news soon reaches the portuguese court in Lisbon. News of exotic naked people, and land untouched by civilization. The goal of spreading christianity was still very present, and this was seen as a great oportunity for that.
This is becoming a huge mess (I am writing this having badly slept the past days, if anyone wants more info on this I can try to help just PM) I will try to sumarize it.
Reasons for Portugal to become interested in colonizing and become a powerhouse were
Geographical location in Europe, closest country to the Atlantic´
No interest in Continental politics
Some argue that it would be the "next logical step" after the trade empire to build a colonial one
Sailing techniques, and a vast knowledge of cartography, navigation, astronomy, and shipbuilding made it easier and more possible to find new places to settle
Spreading the faith and subdue the "infidels".
Here is a bit of backstory and some of the reasons why one (small) country in western Europe decided to colonize, expand and build the first global empire. Your answer may come from seeing the reasons of the other countries that also became interested in colonization. Or matching these reasons to the ones who didn't.
PS: I am sorry for the many grammar and phrasing mistakes I made, I might edit this after I get some sleep. Sorry for the long post, and sorry for murdering the English language.