The Anti-Federalists believed in a "loose" interpretation of the Constitution, since they wanted the Federal Government to have more control over the individual states, meaning that they wanted the powers that were not explicitly stated in the Constitution to go the federal government.
The Federalists also favored a LOOSE construction of the Constitution, believing that the Federal Government should possess all powers not specifically denied to it.
The Anti-Federalists wanted to limit the Federal government STRICTLY to the powers which the Constitution specifically delegated to it. In other words, they wanted to shackle the powers of the government and keep a tight control on it.