The Portuguese went straight to Conte at the final whistle and spent several seconds talking into his ear.
Neither manager would reveal the contents of the conversation but Sky Italia said Mourinho told Conte in Italian: You dont celebrate like that at 4-0. You can do it at 1-0, otherwise its humiliating for us.
Conte gestured to the crowd to turn up the noise levels after NGolo Kante scored Chelseas fourth goal.
British media reported that the ill-feeling spilled into the tunnel where a member of Mourinhos staff refused a handshake from Conte, and others were involved in verbal disputes.
Chelseas manager denied that he had been trying 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 didnt do anything to humiliate Mourinho.