"...whatever is agreed 50% of the country will be disappointed with it."
If anything, a referendum is the ultimate democratic process. There are usually two options, and the one that gets the most votes wins. There's not much point in people saying (as some do) that those who voted one way did so without being in full possession of the facts. Both sides could say that, and they would both be right.
Whenever there's a General election lots of candidates offer themselves to the electorate, and I would hazard a guess that the majority of people vote with their hearts, rather than their heads. No doubt most people did that in the referendum - they based their vote on a gut feeling, and perhaps on something they had read or seen on TV.