The French fighter gave a good account of himself against the WBA and IBF heavyweight champion at Cardiff's Principality Stadium.
Referee Phil Edwards, however, stopped the contest in the 10th round with Takam still standing, prompting some boos from the crowd.
Asked if he thought the ref's decision was correct, Takam told reporters: "I don't think so. I want the rematch if Anthony gives me it. He is a great champion."
Joshua, meanwhile, said: "I have no interest for what's going on with the officials. My job is the opponent.
"I don't have control over the ref's decision. It was a good fight until the ref stopped it. I have the upmost respect for Takam."