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".