If I recall correctly, all advisory referendums in the UK have been winnable by a simple majority.
I imagine there would have been an outcry if the bar for leaving the EU was set higher than 50% of voters, especially because the 1975 referendum to remain in (what became known as) the EU had a 50% threshold to succeed.
It's natural that the people on the wrong side of the result feel a bit aggrieved. This is true in any voting system, for any vote - but can induce relatively severe regret for long-lasting or wide-ranging decisions.
The only solution I can suggest in order to minimise regret is to adopt a strategy of "deciding how we decide" as a preliminary step before the actual vote to decide. (The "Remain" camp were fairly sure they'd win the vote, and foolishly neglected to consider this.)
This approach can also be useful in meetings where a technical decision needs to be made. For instance, it might often be preferable to adopt a consent-based process rather than a consensus-based process. See here: https://en.wikipedia.org/wiki/Consensus_decision-making
Agreeing how to decide something can also be useful in adversarial negotiations, where it is often easier to agree a "fair process" leading to a result than it is to immediately try and haggle about the result itself. (For example: "Will you pay me the average of 3 repair quotes for the damage you did to my car?" vs "Pay me XYZ for the damage you did to my car.")