Conte called Mourinho a "little man" earlier this month after the United boss brought up his suspension as part of a match-fixing investigation while he was with Juventus.
Now, Mourinho aimed another jab at the Italian, claiming on Sunday that he didn't start the bickering and that Conte should stop acting like he's the victim.
“When I start [feuds] I take the responsibilities of that, and I’ve started [them] many times," Mourinho said.
"When I don’t start it’s quite funny for me to see other people on the other side acting like victims when they’re not the victims. But, really, I don’t enjoy. That’s why for me it’s over.”
Conte also has referenced Mourinho's past shots at Claudio Ranieri, before the Portuguese wore a shirt with the former Leicester City boss' name on it when he was sacked.
Mourinho now admits that at times the feuds with other managers have been his fault, but says the Ranieri instance just proves that he's willing to be the bigger man when he knows he's in the wrong.
“Yeah, sometimes it’s my fault,” Mourinho said of the rows.
“Sometimes it’s other managers’ fault. In my case, when I think it’s my fault and I should behave in a different way I’m the first one to apologise, like I did with Ranieri when I had the chance.
“That’s when our relations went from bad to good and from good to very good, because I was man enough to apologise.”
Mourinho and Conte will meet face to face on February 25, when Manchester United and Chelsea face off in the Premier League.