Not entirely. The Preamble reads:
We The People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America.
The Constitution is a delegation of power to the national government, by the people. It's also a limitation on that power, and in some cases on the powers of the states as well. (States can't print money, or levy export taxes for example).
The states role lay in ratification. They didn't write it, but are a party to it because of ratifying it. Since they didn't make the agreement in the first place, they can hardly have made it between them.