The crowd in Cardiff erupted in a chorus of boos when the challenger was stopped in the 10th round, with Joshua having already knocked him to the canvas in the fourth.
Takam, 36, looked in trouble – battered and bruised – in the latter stages of the fight, but was on his feet when the ref called it a day.
Now the Cameroonian, who is a French citizen, has said he would love a rematch against Joshua… if he’ll give it to him.
“I don’t think they should have stopped it,” The Sun quoted Takam as saying on Sunday. “I don’t think they should have stopped it.
“I want the rematch if Anthony gives me it. He is a great champion.”
Takam had some of his best moments of the fight in the seventh round as he repeatedly caught Joshua.
Joshua tried to regain momentum in the eighth with two left hands that shook Takam, who was inspected by the ringside doctor at the start of the ninth round.
Takam was allowed to fight on but in the tenth he was shook by a right to the head and as Joshua unloaded more punches that landed flush, referee Phil Edwards stopped the fight.
Takam was drafted in as a late replacement opponent at 12 days’ notice after Bulgaria’s Kubrat Pulev injured a shoulder.
On the fight, Joshua said, “I come to fight, I don’t sit on the edge and make decisions.
“It was a good fight until the ref stopped it – I have the utmost respect for Takam putting on a good show.
“(Deontay Wilder fight) has to happen for sure. But it comes to a decision where the IBO, WBA and IBF that have mandatories.
“Providing I am free, I can’t fight Joe Bloggs from anywhere – I have to fight championship fighters. These are fighters I have to compete with.
“Now there are belts on the line there are obligations as champion, and once I fulfil those my door is open to any challenger. It’s no problem.”
The 28-year old suffered a damaged nose before breaking down Takam for a 20th-consecutive knockout victory.
Former super-middleweight world champion Carl Froch says he understands why the referee stopped the fight, but that doesn’t mean he agrees with it.
“He was definitely saved from further punishment,” Froch told Skysports.
“I think the sensible people that watch boxing would not argue with that stoppage.
“The barbarians, and I’m a barbarian – I like barbaric finishes and I have always done. But the fight could have gone on so it’s subjective.”