Why Isn't Prohibition Considered Unconstitutional?

OK, here's the thing I really don't get. Remember a thing called Prohibition, when we as a nation did a War on Drugs kind of thing with alcohol? It worked just about as well as the current War on Drugs, and was recognized as an enormous failure and canceled after only a few years, but that's not my point right now. My point is this: making it illegal to consume a substance was a clear violation of the freedoms that we in this country rightfully hold so dear, so in order to wage a War on Alcohol, congress actually had to change the Constitution in order to outlaw drinking. And, of course, when we as a nation wised up and put an end to that Bad Idea, another amendment had to be added to the Constitution to cancel out the previous one that had made consuming alcohol illegal. At least that's what I remember from my high school civics class.

So my question is, how can pot be illegal without an amendment to the Constitution?

I've heard the official answer to this, and it's something like this: Prohibition made consumption of alcohol illegal, but the War on Drugs instead targets the possession of illicit substances. I guess this means it was clear, at least back in the 20's, that we have the right to control what happens to our own bodies, and in order to take that right away, the Constitution had to be altered, but when they wanted to do it again, they skipped the whole amendment process by saying it's illegal to possess the stuff instead of making it illegal to use it.

It seems to me that this is the legal equivalent of cheating. If it was necessary to change the Constitution in order to outlaw booze, I don't see how you can legally outlaw other drugs without a similar change to the Constitution. The Constitution gives us all certain rights, and from a legal standpoint, I see no real difference between the right to consume booze and the right to consume pot.