And are you actually saying that such important decisions shouldn't be left up to voters? If so, then should choosing leaders be left up to voters?
It seems pretty clear that many (not all) of those who voted Leave were in fact telling the EU and the scaremongering demagogues for Remain, "Fuck you." And some other portion (the sets probably overlap) were saying something like, "This EU thing isn't working out like you said it would, so we want out." Not, "I don't know what I want."
I think the population has a right to vote. I just don't think most people are fit to vote on every particular issue. It's en emotional vote and it could have swung one way or the other. Interesting times!
Not entirely sure of your general opinions on voting, but for the most part, majority is majority when it comes to democracy. You can't now claim "oh but it isn't victory by a significant margin, therefore people didn't really know what they wanted to vote for." The message is: "52% of the voters at the time wanted X, therefore democracy-dictates we do X". If it's good-enough for electing our leaders, it's good enough for a referendum.
The British people didn't say "fuck you", they said "we don't really know what we want". I mean, 52-48 is not insignificant, but it's also not a "clear, strong message" for leaving - it's a message from a divided nation who is quite literally not sure what it wants. Just sit in a restaurant tonight and look around - whatever your opinion, half of the customers agree with you.
The issues at hand are very complex and quite simply too much so for most voters to even get an idea of what's at stake. As with any such referendum, the overwhelming majority of the votes are cast emotionally. You cannot get such a massive amount of people to think through the implications rationally - they go with their gut.
So again, the message here is "we have no idea what we really want", not "fuck you".