Here's the thing. I used to ask the same question of why Italian states never attempted colonization efforts whereas some states of similar economic and military and economic power such as The Netherlands and Sweden did.

First off, the initial reason for colonization and exploration of the Americas and Africa was to get around The Ottomans. The Ottomans did control Europe-Pacific Asia and Indian trade, and had a tendency to cut off trade or charge high tariffs for commodities when it suited their political aims. Venice and the Ottoman Empire have an interesting history with high volumes of trade interrupted by brutal warfare and conflict over Mediterranean Islands.

The thing is the Italian states, The Ottoman Empire, and to an extent Russia had the same problems and perks. All three had almost no access to the Atlantic Ocean geographically. No access to Atlantic means resupplying a colony is impossible, and Spain's control of the Straits of Gibraltar are the prime reason why they were the only Mediterranean power besides France to colonize the Americas.

Next the former two already had access to Asian commodities. Most European countries bought these products from Italians who bought them from The Ottomans at such a volume that Italy and Lebanon both developed their own domestic silk industry.

The Ottomans in particular had no need to conquer the New World. Their explorers 'discovered' Indonesia for instance, and converted many of what are now Indonesians to Islam. They did, in a sense, practice forms of colonization in Central Asia, Southern and East Africa, and in the subcontinent and South Seas wherever they could. We don't have as detailed records and I'm not entirely sure why but they also practiced aggressive trade and chattel slavery in a similar fashion to the early Western European imperial projects of Atlantic-based powers.

Finally the discovery of the New World in no way affected Ottoman trade until about the 1800s. The Americas weren't Asia, all they served was to provide Europeans with monopolies on rare and valuable commodities putting them on an economically equal playing field to the Ottoman Turkey, Safavid Iran, Mughal India, and Ming China. The Naval expenditures required to maintain American colonies gave Europeans their first technological advantage vis a vis these other powers. Add to that the antagonistic nature of international commerce and you have pretexts for conflict, and better ships means higher volume of trade and quicker and more efficient resupply of a colony or military expedition which lead to the defeat of the Asian Empires.

Edit : Now corrected error, the Ottomans did not discover Indonesia for the Muslims of West Asia and North Africa, Arab explorers had already visited Indonesia and Southeast Asia and converted inhabitants to Islam before the Ottomans began launching expeditions in the region in a colonial conflict with the Portuguese.

Edit2: Non-Wiki sources for all info from this thread:

Capponi "Victory of the West" 2006

Bicheno "Crescent and Cross the Battle of Lepanto 1571" 2003

Kurlansky "Salt A World History" 2003

Heers "The Barbary Corsairs Warfare in the Mediterranean 1480-1580" 2003

Murphey "Ottoman Warfare 1500-1700" 1999

Weatherford "Genghis Khan and the Making of the Modern World" 2004

If you are really interested, the book by Giancarlo Casale "The Ottoman Age of Exploration" look into this question.