Norway also had a vote on the EU. I was also close. "No" won.
What Norway didn't implement was a "winner takes all" approach. They're not in the EU. They're not in the Customs union. They are in the EEA. Everybody wins, everybody loses, but nobody feels like their wishes have been completely ignored.
There is no reason the results of the Brexit referendum couldn't have been interpreted like that. It's not like there's only one seat that can be filled by one person and there has to be a loser. It's not an election.