Why did Europeans, and not Asians, undertake the voyages of discovery connecting Old World with New World?

Considering that much of the technology that permitted Europeans to traverse the oceans came from Asia and the Far East, the reason is not found in any technical advantage that Europe possessed over Asia.  In answering this question, it is important to understand the motive for European exploration and discovery of America.  First, the Europeans wanted an easier and less expensive route to the East in order to acquire spices, drugs, perfumes, and silks that were in very high demand on their continent after the Crusades.  So through this perspective, the Asians would not be trying to find a sea route to their own lands.  Secondly, the Europeans were in the midst of the Renaissance, a period of time in which there was a belief in the unbelievable potential of humanity. This period brought about scientific discovery and reason.  Despite the fact that Europeans discovered a previously unknown world, this was done by complete accident and for years following the landfall of Columbus, Europeans still did not realize they were not in Asia.