But he said in the days leading up to the fight that he will not fall into the trap of trying to fight Triple G toe-to-toe.
Golovkin fell to 38-1-1, with 34 knockouts.
Golovkin, the big puncher from Kazakhstan, has gone the distance twice in his last three fights, including the draw with Alvarez.
"If the people want another round, I'll do it again", said Alvarez, who improves to 50-1-2. He's a great fighter but in the end I got the victory.
"I think he's scared".
Gennady Golovkin and Canelo Alvarez exchange punches during their WBC/WBA middleweight title fight at T-Mobile Arena on September 15, 2018 in Las Vegas, Nevada. He was credited with landing 234 of 879 punches while Alvarez landed 203 of 622. Great fight with two great champions!'
The 12th was exceptionally close as the men battled on even terms. If the third fight does happen, you would imagine it would happen back here in May next year. "For now I'm going to enjoy it with my family".More news: Eliud Kipchoge smashes marathon world record in Berlin
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The fight was stopped at 1:03 of the third round.
Golovkin, whose first defeat comes in his 40th bout, left the ring immediately without conducting an interview as his rival - fighting for the first time since serving a six-month drugs ban - celebrated.
"One of the best fights I've ever seen", tweeted James.
"Some very close rounds that could have went either way".
Gennady Golovkin suffered the first loss of his professional career when Saul "Canelo" Alvares won an epic middleweight world title fight in Las Vegas on Saturday. The pair was originally scheduled to rematch on May 5 until a pair of alleged positive tests for clenbuterol lead to Golden Boy Promotions withdrawing Canelo from the fight.
"We knew the best way to beat him was to make him go backwards", Alvarez said.
'I pushed him back, it was me who was aggressive.