A majority should always take priority of the minority regardless of how small the difference between the two.
The tyranny of the majority. It's just about acceptable for general elections as it's not a once-and-forever decision, a renewal of mandate is sought to a schedule under the Fixed Term Parliament Act. But our first-past-the-post duopoly is one of the most backwards democratic systems in the Western World. It's anti-compromise.
The problem here is that the option presented was Remain/Leave binary choice. But neither option was that clear-cut. Just look at the Leave campaign's pre-referendum statements and campaign materials, they were very clearly in favour of remaining in the Customs Union and for negotiating the post-Brexit relationship with the EU before triggering the actual leave date.
An equivocal referendum result (see Farage's statement on 52:48 made before the result was announced) was not a clear mandate for a hard Brexit and leaving every European institution, agreement, and treaty. Theresa May has interpreted it as such in part to hold her party together, but mostly because she's always had issues with immigration and was frustrated in the Home Office by human rights legislation.
The marginal result of the referendum was just about justification for a Norway-plus option, something that would have made both sides of the argument equally unhappy but without the dramatic dummy-spit shocks to the economy.
If it had been the same marginal result but the other way, it would have been a good mandate for seeking reforms to the EU from within. And would probably have support from many of the southern EU members and popular support from the electorates of France and Germany too.
I'm not entirely sure what the post-Brexit arguments will mean for the UK. But I suspect that no matter what happens in the next few weeks the UK electoral system has taken a massive loss of trust. It's broken and needs to be fixed.