Neither fighter was knocked down nor seriously hurt during an absorbing, and hugely-anticipated, bout for the WBC, WBA and IBF middleweight titles at the T-Mobile Arena in Las Vegas.
A close contest was declared a draw but Byrd has come in for heavy criticism after awarding Alvarez 10 of the 12 rounds in a 118-110 verdict.
Fellow judge Dave Moretti gave Golovkin the nod 115-113 while Don Trella could not split the combatants as he returned a 114-114 result.
Golovkin was incredulous and reasoned that he landed more punches overall – 218 to Alvarez’s 169 according to CompuBox statistics – and the fact that a portion of the pro-Mexican crowd booed the result as evidence that Byrd had erred.
The Kazakh said: “I saw computer, all total punches, I saw people’s reaction.
“It’s terrible, for me it’s terrible. This is not correct, this is very bad for the sport.”
Alvarez’s promoter Oscar De La Hoya felt his charge won but he too was aghast at Byrd’s decision, which caused a stir on social media with former world heavyweight champion Lennox Lewis among those to express his disgust.
De La Hoya said: “These guys fought their heart out, Gennady is a tremendous, tremendous champion and Canelo’s a tremendous, tremendous champion. Everybody has their opinion but that’s what made it such a great, great fight.
“The 118-110, I don’t understand, I really don’t. Byrd is a very competent judge but I just don’t understand 118-110. I had Canelo winning seven-five. 118-110 is a shocker.”
Alvarez also felt he had done enough to prise the middleweight straps away from Golovkin.
Speaking through a translator, the 27-year-old said: “I didn’t base it on the scorecard, I wasn’t taking points round-by-round but what I am sure of at the end of the fight was that I won. I have no doubt in my mind, I won the fight.”
Alvarez – whose record now stands at 49 wins, 34 inside the distance, with one defeat and two draws – largely fought on the back foot in an effort to neutralise Golovkin’s much-vaunted power.
Following a cagey opening couple of rounds, it seemed a tactic that would backfire with Golovkin forcing the issue behind a dominant jab but Alvarez finished strongly – winning the last three rounds on all of the judges’ scorecards.
Golovkin (37-0-1, 33KOs) chastised his Mexican foe for his tactics, with the 35-year-old saying: “He talked too much before the fight. He said he’s a true Mexican man (and that he would) bring Mexican style.
“(But) he moved every round, moving, not staying.”
The disputable decision means a rematch becomes a tantalising prospect, one Golovkin would relish as he said in the ring afterwards: “Look at my belts. I’m still the champion. Of course I want a rematch.”
Alvarez also seems keen, adding: “Yes, of course, obviously yes, if the people want it, yes.”