When you say "East Asian empires", I assume you either mean Ancient China or Japan. In the case of Japan, the answer is rather simple. What fueled the Age of Colonization (at least in the case of the earliest colonial power, Portugal) was arguably the desire to discover an alternate route to India and the lucrative spice trade by circumventing the Ottoman Empire. Japan had no desire to do so because it already had two lucrative trading partners as next-door neighbors: China and Korea. Whatever Japan lacked, it could source from these two countries by trade (or later, conquest). Furthermore, Japanese vessels were not built for ocean-going voyages, so therefore their maritime technology was not even capable of doing so. And by the time when the Age of Colonization was at its peak heyday, the Japanese, by the mandate of the ruling Shogunate, closed itself off to outside powers by choice - an isolationist policy known as "Sakoku" (鎖国). This only ended in 1853 when the "Black Ships" of Matthew Perry from the USA forced the Japanese to open up. By that time, the Age of Colonization was pretty much over.

In the case of Ancient China, it becomes more complex. Certainly, the Chinese had the technology, and the resources, to do so. In fact, they had a great fleet that was thought to be capable of it from 1405 to 1433. Specifically, from 1405 to 1433 the Ancient Chinese (under the Ming Dynasty at the time) constructed a massive fleet, probably far larger and more powerful than anything the world had ever seen up to that point. Under the command of Zheng He, this fleet visited much of Southeast Asia, India, Arabia, and even southern parts of Africa. The key word here is 'visited', not 'explored'. The routes undertaken by this great fleet were well-established and known to the Chinese, and by no means new.

Why didn't this great fleet turn to the Northern Pacific coastline then? Well, for one thing, the Chinese expeditions led by Zheng He were going through known routes. Back then, the Chinese probably had no idea anything existed in the east past Japan. Nor, I imagine, were they keen on building a vast fleet and sending it sailing into the great unknown. They, like the Japanese, had no incentive to do so, particularly after the expeditions they undertook. The rich lands sought by the Europeans (which some say inadvertently led them to discover the Americas) were right next to China, so why explore into the great unknown?

It is also important to note that while the Europeans sought lucrative trade, the Imperial Chinese attitude means that while they knew of the existence of Europe, they probably doubted Europe had anything to offer them. You can evidence some hint of this attitude from the reply from Emperor Qianlong to King George III, which you can view in detail (a translated version) here: http://academics.wellesley.edu/Polisci/wj/China/208/READINGS/qianlong.html

Sources:

1. Wade, Geoff. "The Zheng He voyages: a reassessment." Journal of the Malaysian Branch of the Royal Asiatic Society (2005): 37-58.

2. Toby, Ronald P. "Reopening the question of Sakoku: Diplomacy in the legitimation of the Tokugawa Bakufu." Journal of Japanese Studies 3.2 (1977): 323-363.