The United boss was furious at the Italian for waving his arms around to get the home supporters going in the 90th minute, when his team were already 4-0 up.
The Portuguese coach reportedly told Conte it was disrespectful and something to do only when your team were leading 1-0 and trying to hold on.
But last night Conte defended his actions, saying he was concerned all he could hear was the travelling support and felt his team deserved some acclaim following their brilliant victory.
Both managers refused to reveal the details of the conversation but Conte looked clearly upset following Mourinho’s outburst.
“There is always been respect for all, and naturally for Manchester United”
Chelsea boss Antonio Conte
“I was a player,” he said. “I know what the feeling is like (to score). I only told the fans to applaud the team because the team deserved it.
“There is always been respect for all, and naturally for Manchester United.
“ I did something absolutely normal. I didn’t do anything to humiliate Mourinho.
“I think that, today, it was right to call our fans in a moment I was listening only to the supporters of Manchester United at 4-0.
“So I called the fans to give the players a great clap after this kind of performance. The players, after a 4-0 win, deserved a great clap. It’s very normal.”
Asked if he regretted doing it, Conte added: “We live with emotions. If you want to cut the emotions, we can stay at home and I will change jobs.
“It’s important for our fans to push in every moment of the game. When the players deserve it after this performance, it’s right to receive a great clap from the fans.”
Mourinho would only say: “I’m not the kind of guy to come here and share with you things I don’t want to share.”
United went behind to a Pedro goal after 30 seconds and looked defensively frail throughout as Gary Cahill, Eden Hazard and N’Golo Kante also got on the scoresheet.
Mourinho added: “Football matches start at 0-0, this match started 1-0.
“It is like giving Chelsea chance to play how they want. Everything went in their direction.”
He also revealed £30m centreback Eric Bailly suffered what is feared to be a serious knee ligament injury.
Mourinho said: “I am afraid he is badly injured in his knee, in the ligament area. He feels that it is really bad.”