The Russian won a unanimous points decision as all three judges scored it 115-113.
But despite dominating the majority of the fight, Bivol wasn’t entirely sure it would go his way after the judges’ scorecards were announced.
During an appearance on the DAZN Boxing Show, Bivol said: “When I heard 115-113, all judges, for one second I thought maybe it’s not my day today.
“When I heard, ‘And still’… they made the right decision!”
Eddie Hearn, who promotes Alvarez and Bivol, had expected the Russian to be a ‘tough fight’ for the Mexican.
And the Matchroom Boxing chief agrees that Bivol should have been awarded the win against Alvarez after he put on ‘a punch perfect performance’.
Speaking after the fight, he said: “We talked going into this fight how good Dmitry Bivol is, how tough this fight was, and it was a punch perfect performance.
“He had to box exactly how he boxed. The judges had it right for me. He won that fight. Did Canelo look a little bit flat? Was Canelo tired? I think it was the brilliance of Dmitry Bivol.
“Like [Bivol] said, he felt like he was a steppingstone to Gennady Golovkin – and he was for the career plans of Canelo Alvarez. What a night for him. He dreamed of this night, got the opportunity.
“There were a lot of Bivol’s fights in the pandemic and through the pandemic, where his performances looked a little bit flat. You look at the fight with Craig Richards and Lenin Castillo before that, those performances didn’t tell you that that form would beat Canelo Alvarez.
“When you have a special fighter like Dmitry Bivol, if you can produce on the night, you can win these big fights. And he produced on unbelievable levels, unbelievable levels. It was the perfect performance at the right time.”