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There's a reason that most functional democracies have a constitution can only by changed by meeting a higher bar than simple majority: it's too important, too sensitive, and too irreversible to be decided without something closer to consensus.In the general case I agree, but I think this vote is a bit different in that it was arguably about reverting another constitutional change - the ongoing abdication of many functions to an EU government with much less democratic accountability to the UK public - which was never legitimized by popular vote at all.
The last relevant UK referendum was the 1975 one on "European Communities membership", and at the time the EEC was pitched to voters as a purely economic arrangement, with none of the aspects of supranational government later introduced by Maastricht. That economic phrasing found just over two-thirds support, while polling conducted around the same time on political integration found (IIRC) just under one-third support.
As far as I know, every time European political integration has been put to a referendum, it's been rejected. The "Treaty establishing a Constitution for Europe" was rejected by the French and Dutch populations in 2005; after that it was temporarily shelved then sneakily repackaged as the "Treaty of Lisbon" in 2008. Ireland held a referendum and rejected that too, but since that was the wrong answer it was forced to hold it again and voters were basically told to vote yes or else.
So the situation is not at all like the formation of something like the USA, where state populations explicitly agreed to political union. Political union is happening against the wishes of national populations. I don't think national leaders, even democratically elected ones, have the right to take power away from the populations they represent, any more than they have the right to say "hey, guess what, we're not going to have any more elections, we'll just stay in office forever".