The modern nation of Germany did not exist until after 1871; at this point, the United States had been long established and was a rising industrial superpower. In the colonial era of the United States, the modern nation of Germany consisted of Prussia and a collection of smaller states. Prussia considered itself a land-based power. Prussia was more concerned with attack from Russia, France, and, before it was partitioned, the kingdom of Poland. All of these things did not allow the kings of Prussia to pursue colonization although many Germans moved to colonial America, especially Pennsylvania where Benjamin Franklin complained about their unwillingness to learn English and assimilate into colonial society.
Another factor that might have influenced Germany's lack of colonization in North America was the Thirty Years' War which ravaged central Europe from 1618 to 1648. This conflict killed over one million people and destabilized the region. This also served as further distraction from any of the German states attempting to colonize North America.
It is important to note that George III, king of Britain at the time of the American Revolution, was a member of the House of Hanover, which was one of the German states. While Germany could not claim the colonies as a possession, the colonies were ruled by a king with strong German ties.