The Brazil international endured a tough debut campaign at Spurs last season under Conte before the Italian was sacked by the club in March.
Richarlison had criticised Conte following Tottenham's elimination from the Champions League round of 16 before the latter responded and described the player as being "selfish."
Speaking to the Que Papinho podcast, Richarlison said he was wrong to have publicly criticised his manager and he received his punishment in front of his teammates.
"Of course I made a fool of myself by saying in the interview that I needed time and everything else, it was after the elimination in the Champions League, but then I apologised to him," Richarlison said.
"I even told him that if he wanted to punish me, he could. We worked it out there, then I tried to have a run again, and another injury came up. Like it or not, it ends up affecting the head as well.
"He has to show his firmness also to the group, to say that he is there, that he is still in charge. It is his way of dealing with people, with the group, and he spent almost two hours just telling me off in the meeting, in front of everyone [laughs].
"Then the players even said: 'Richi, don't do this anymore. Stay two hours waiting' [laughs]. Everyone wanted to go, and we were there. Solved, fine."
Following Conte's dismissal, the 26-year-old said he reached out to the Italian to clear the air.
"After they sent him away, I sent him a message," Richarlison added. "I apologised because he was the guy who asked for me to be hired, and I couldn't help him as much as he thought I could. The least I could do is apologise for what happened there."