Would you have allowed a referendum in the first place? If not then you can't really say that you wanted more democracy. I'm sure you're of the view that the majority of the electorate are too stupid to be allowed to vote at all.
The referendum simply asked do you want to leave the EU and that's it. If somebody wanted to leave the EU and they voted to leave the EU and then we left the EU then that referendum has been satisfied. Their reasons for wanting to leave are far too complex to be reduced down to lies. My father in law was a hard line Brexiter and his mind was made up long before the referendum was even held.
It was also impossible that anybody could have voted for a realistic Brexit because the EU would not allow any pre-negotiations so a well-defined version to vote for could never exist. So for those who wanted to consider a serious Brexit then what were they going to vote for other than an optimistic view?
The definition of Brexit, ie the negotiated version only began once we triggered Article 50 but unfortunately the Tory government did that without any knowledge of what it wanted to negotiate. They then LOST all authority in Parliament and our position was compromised to essentially salvage anything that could be salvaged.
I don't see why any of this is the fault of the people who voted for it. It's the fault of politicians, Parliament and the political system which gave us this end result. And what sums up this awful end result? Theresa May was given a peerage!