To begin with, the very reason why Tokugawa Japan cut itself off from most of the outside world was because of European exploration. The century leading up to the Edo period (the era of the Tokugawa Shogunate, 1603-1868) was one largely filled with war. One factor which had helped some sides, though, was the arrival of Europeans, most notably the Portugese and Spanish. Several Daimyo found that they could gain advantage by heeding the often Iberian Jesuit missionary's calls to convert to Christianity, and in exchange they would often receive military or monetary support.

When the Tokugawa succeeded in taking control of a united Japan, one of the paramount measures used to implement stability was the establishment of a system of absolute loyalty to the Shogun. Other measures included the requirement that all other lords spend every other year in Edo (modern Tokyo) and leave their families behind when they weren't there; an incredibly expensive endeavor as i both required them to construct lavish Edo estates and pay for a large retinue to go back and forth regularly. The isolation was intended to prevent Daimyo from cultivating outside loyalties, either to the Church itself or to a foreign power, who might be able to help them subvert the Tokugawa rule. The early years of Tokugawa witnessed the hundreds of thousands of Christians persecuted and either killed or forced to recant their conversion, as well as several uprisings by Christians; by the middle of the 17th century though, Japan's christians had either recanted, fled to other countries, or gone into isolated hiding.

However, its a misconception to assume that Tokugawa Japan was entirely cut off from the world. A Dutch trading post. Dejima, was permitted to stay on an artificial island off of Nagasaki, and through here a substantial amount of Rangaku ('Dutch Learning') found its way into Japan. The Dutch were chosen in part because they were the other main power so far east at the time, but also because, unlike the Iberian powers, their interest was solely in trade and had little interest in spreading religion.

Many Rangaku scholars would, in the final years of the Shogunate and in the Meiji period, have great influence as they had already developed a foundation for European knowledge. One very famous one, Fukuzawa Yukichi (the founder of the prestigious Keio University) noted on the first diplomatic mission to America in 1859 that he was hardly impressed by the technology itself that he saw; most of it he was already familiar with through reading books imported through the Dutch. Rather it was the cultural aspects of America (and later other Western nations) that fascinated him.

The existence of this large body of European-derived knowledge is believed to be one of the major contributing factors to Japan's speedy industrialization following the fall of the Shogunate as it offered Japan a foundation to build on.

This question is based on a false premise. The Tokugawa government did not start to seclude the country until the 1630s, by which time Europeans (specifically Portugese) had been doing business with Japanese merchants for nearly 80 years, and by which time the "Age of Discovery" might be said to have been over for at least a little while.