Whatever the result of the referendum, the future would be worse than the present. It was just a case of deciding whether the UK wanted to have a worse future within the EU, or a worse future outside of it. The present isn't all that great, but the future would have been worse however the public had voted. Like the US election, the choice was effectively "would you rather get shot or be stabbed?" There was no "right" or "wrong" choice, there were just two "wrong" ones.
The point of a democracy is that people make decisions that others don't agree with. I would rather live in a country where the public make "wrong" decisions than a country where the public have no say in who runs the country or what they do.
It's like the neverendum in Scotland. I think it would be bad if they vote to leave the UK - bad for Scotland, bad for the rest of the UK - but if they choose to do so in the second referendum, the third referendum or whenever - that is the choice that the Scottish public make. But whatever the outcome, people who voted the other way will have to live with the consequences.
Think of the disaster that was Tony Blair and "New Labour". People were passionate about kicking the "evil Tories" out and expected a better future. What a let down that was! Blair introduced Student Loans, saddling students with debt. Blair allowed the country to rack up obscene levels of debt. He did more damage to the country than anything the "evil Tories" had managed, damage that the country will be paying for for decades to come. And that was with 43.2% of the vote in 1997, 40.7% in 2001 and 35.2% in 2005. A mandate to run the country from well under half of the voting public. So when we have a referendum and something is favoured by the majority, we have to accept it.