How else do you want democracy to work? The people agreed on a system of rules order to decide between two directions and a decision was made. If the government can just decide to not carry out the will of the people (however thin the margins are) then why have a vote at all?
Perhaps more than a simple majority? Perhaps a majority of the eligible voting population? What is called a "razor-thin majority" is actually a plurality. And I don't think democratic decisions should be made by plurality.
I want parliament to do its job we elected them to do. I want it not to use referendums to make major far-reaching decisions on simple majorities. We elect representatives to govern on our behalf not ask us what to do with a referendum at every turn.
I wonder if for things like joining our leaving the EU we should make them get at least 60ish percent of the vote. Simple majorities have a tendency to ping-pong back and forth so it doesn't seem optional for huge systemic changes.
I'm not suggesting moving the goalposts now. I'm just saying the whole thing was misconceived in the first place.
Cameron, when he called the referendum, never beleived it would go Leave. All the polls at that time said Remain would win easily. He believed it would be a clear Remain and we would all move on.