A narrow result in a referendum about the constitution should always require a meaningful quorum. In most countries election results are regularly decided by the thinnest of margins. But the UK referendum about Brexit leaves a somewhat sour taste as the majority of 52% has defeated a minority of 48%. So there is quite a split among the citizens, and a different result would just have meant that the roles are reversed.
There are several lesson from the whole exercise:
The development of the EU and its institutions proceeded with little regard to the wishes of the electorate. Regular consultations on major steps forward should have been submitted to a referendum in all the member states, with a significant quorum (2/3?) as safety valve.
It should not be at the pleasure of a Politician whether or not a referendum takes place. If we want to live in a proper democracy the consultation of the citizens should be governed by mandatory and predictable rules. Otherwise the often mentioned objection to Direct Democracy - that it can be abused by Governments and referenda become plebiscites - will always have to be taken seriously.