What is again being conveniently forgotten in the claims that we should have left this to parliament is the reason we had the referendum. In our (effectively) two-party state, both parties were in favour of remaining in the EU, meaning that the many people who disagreed with our membership had no opportunity to be represented.
Along came UKIP, and they started getting sufficient votes that the only way they could be stopped was by the promise of a referendum.
The result of the referendum showed just how large a proportion of the voting electorate had previously been disenfranchised by the two-party system.