What did antifederalists believe the Constitution was lacking?

Supporters of the Constitution were called Federalists, a name that was chosen with care. It emphasized that the constitution would create a federal system. Federalists believed that that power should be divided between a central government and state governments. They hoped their name would remind Americans who feared the central government that the states would retain many of their power. However, the opponents of the Constitution were called Anti-Federalists-a misleading name, as they were not against federalism. They instead accepted the need for a national government, but the real issue for them was whether the national government or the state government would be supreme. Anti-Federalists believed the New Constitution should have included the bill of rights.

Anti-federalists are the delegates who believed that the state Governments be conferred with more powers than the Central or the Federal Government.

Explanation:

The Anti-federalists felt that the Constitution provided undue powers to the legislature and the president' rights of pardon and elastic clause, this made the anti-federalists to plea for the prerequisite of Bill of rights which the federalists approved upon.

In order to give heed to and conciliate the anti-federalists, bill of rights was an auxiliary in the constitution. Federalists were the people who believed in strong Central Government. George Washington and Alexander Hamilton were federalists. Anti-federalists are the personalities who had a sturdy conviction in strong state Governments; they were James Madison, Thomas Jefferson.

It was Madison who propounded his idea of giving equal authorities to both states and Central Government and he introduced the system of checks and balance and equal delegation of powers.