Regardless that the US Constitution opens with "We the people," it wasn't the people who created it, it was the states. 

It was state representatives who produced the constitution and it was the states who ratified it. This was clearly understood at the time and for a long time after.

And, very importantly, the states retained their power under the constitution. I could throw a number of quotes at you to support this, but I'll give you just one, leading into our main point. It comes from James Madison, the primary author of the constitution, in the Federalist Papers (#39, to be specific). This is Madison explaining the power of the states over the Senate in the new arrangements:

The Senate, on the other hand, will derive its powers from the States, as political and coequal societies…

Notice that Senate got its powers directly and only from the states. 

Senators, under the original constitution, were appointed by state governments, not elected by the people. This was a crucial part of the arrangement. In fact, this was the original separation of powers. I'll state that again, because it's a completely novel thought to most Americans, and deeply important:

Giving the states control of the Senate was the original separation of powers. This was done carefully and thoughtfully, to prevent the consolodation of power in Washington, D.C. 

Under this arrangement, the states kept the Senate, with its very broad powers, under their control.

Again I could throw out quotes on the importance of breaking up power to the framers of the US constitution, but I'll leave that job to you. I will, however, summarize this point:

The purpose of the states having the power to appoint senators wasn't to deprive the people of a voice, it was to protect the people by preventing the centralization of power.

This crucial arrangement held, more or less, until the ratification of the seventeenth amendment in 1913. And it's important to note that the arguments in favor of that amendment played upon ignorance and gullibility.