One of the biggest reasons Jefferson opposed the creation of the national bank was the fact that this power was not explicitly given to the federal government in the US Constitution.
At his core, Jefferson believed in a strict interpretation of the Constitution. He felt that in order for the federal government to have the ability to take an action, that action must be written down in the constitution. If it was not written down in the Constitution, he argued that the government did not have the authority to do it. He felt this concept would help to limit the power of the federal government.