Jefferson was a strict constructionist of the Constitution, which basically meant that he wanted to follow a strict interpretation of the Constitution itself. That means that he wanted to follow it word for word or follow exactly what the document said.
Being an Anti-Federalist, Jefferson was not really in favor of the Constitution in the first place, so as a result, he believed that if he had to follow this document that he didn't agree with, he believed he should have to follow it word for word if it should be followed at all. Most of the Anti-Federalists preferred the states to have more power than the government, so it was difficult for the Anti-Federalists to accept the Constitution.
That's why the Bill of Rights was helpful when it was written as it directly addressed the rights of the people in the Constitution.
