We have MP's because we have a representative democracy and generally this works reasonably well. But it works less well on constitutional matters that cut across party lines. No mainstream party has advocated leaving the EU in the last few decades so unless you wanted to vote for UKIP (which I didn't) then you were disenfranchised on the issue. Parliament voted by 6 to 1 to give the vote to the people, and they gave their verdict.
As for your 62.5% statistic, you can just as easily say 65.5% did not vote to stay in the EU.