I think the EU should simply improve its outreach programs. Some of them were very successful (Erasmus), some weren't (the EU flag on buildings is almost imperialistic).
The truth is that getting 511m+ people to agree on things, when they won't even speak the same language, will always be a huge challenge. Unfortunately, there is no alternative: this planet has to learn to resolve its problems by talking and agreeing a common course of action, so might as well start with your immediate neighbours.
Now, other member states did hold referendums on these changes, of course - and in some cases, their voting public ended up rejecting those changes. They went ahead anyway, usually with some tweaks to the language used to describe them but very few substantiative differences.
That's utterly false.
Ireland (twice) got legal guarantees that the scary scenarios evoked by the rejectors, would never happen.
Denmark obtained opt-outs, again listening to concerns and guaranteeing that they would never happen.
France (and basically the Dutch) literally re-negotiated the whole treaty.
Those are substantive changes. I don't know how more substantive you can get than "if we make a law you don't like, you're free to ignore it" and "ok, we'll do it again from scratch".
And now the immediate implications of leaving the EU are much greater than the immediate implications in 1975 of joining a customs union, so even if a 50%+ referendum was enough for a customs union, a strong argument can be made that leaving the EU should be held to a higher standard.
I think the main takeaway of this experience should be this: the EU should never accept new members unless there's durable majority support in the member country for being a part of the EU. One plausible version of this is 60%+ support in two consecutive elections.