Charlo (34-1-1, 18 KOs) caught Castano napping on two occasions during the fight but the Argentine appeared to have done enough to win on points.
Charlo, who claimed after the contest that he had 'won this fight' and 'hurt him a lot more', refused to rule out the possibility of a rematch with Castano.
And Charlo's co-promoter Al Haymon has also said that the Louisiana native wants to put right the wrongs against Castano.
But Canelo Alvarez has hit back at Charlo's claims and suggested that Castano was robbed of victory after his undisputed clash against Charlo was declared a split-decision draw.
"Brian Castano, I'll tell you one thing. For me, you won," Canelo said on a FaceTime call with Castano on Monday.
"They [the judges] saw a draw, but for me, you won, you b------, what a great fight.
"I congratulate you very much."
Castano replied by saying: "Thank you very much, brother."
Although not yet officially confirmed, Mexican Alvarez looks set to take on undefeated American IBF super-middleweight champion Caleb Plant in September.
The 31-year-old has also previously expressed an interest in facing Charlo's identical twin brother Jermall Charlo after the American beat Juan Macias Montiel last month.
“Jermall Charlo’s time is coming. I’m focused on Caleb Plant first," he said. ”It’s almost time for Jermall Charlo and Canelo Alvarez to fight."
Speaking on the DAZN Boxing Show, Sergio Mora said the sky is still the limit for Mexican fighter Alvarez.
Canelo currently occupies top spot on GIVEMESPORT's latest pound-for-pound rankings.
The former super-welterweight champion believes the 31-year-old is quite capable of beating both light-heavyweight champions Artur Beterbiev and Dimitry Bivol.
“That fight with [Sergey] Kovalev was a calculated risk,” said Mora.
“If he fights Beterbiev it’ll just be a flat-out dangerous risk, but that's what Canelo likes to do. He likes to surprise boxing, but with the biggest fans and give the fans what they want.
“Whenever people talk about fighters, champions not giving the fans the fight they deserve. This is what they're talking about.
“I’ll become comfortable with either Triple B - Beterbiev, Bivol, [David] Benavidez, either way, Canelo does take on the best.”News Now - Sport News