The Portuguese went straight to Conte at the final whistle and spent several seconds talking into his ear. Neither manager revealed the contents of the conversation but Sky Italia reported Mourinho told Conte in Italian:
"You don't celebrate like that at 4-0. You can do it at 1-0, otherwise it's humiliating for us."
British papers reported that the ill-feeling spilled into the tunnel where a member of Mourinho's staff refused a handshake from Conte, while others were involved in verbal disputes.
Chelsea's manager denied that he had tried to humiliate United.
"There has always been respect for all, and naturally for Manchester United," said Conte.
"Nothing happened. I did something absolutely normal. I didn't do anything to humiliate Mourinho. The players, after a 4-0 win, deserved a great clap. It's very normal. We live with emotions. If you want to cut the emotions, we can stay at home and I will change jobs."