Mourinho, speaking after United's 1-0 win in Lisbon on Wednesday night, did not name names but it was clear he was thinking of his former club Chelsea and Conte, his successor as boss, when he talked of other managers who "cry and cry and cry" about injuries.
And, when the subject was broached after Chelsea's 3-3 draw with Roma, Conte retaliated.
"A lot of time Mourinho has to see what happens at Chelsea," Conte said.
Chelsea's Italian head coach Antonio Conte gestures during a UEFA Champions league group stage football match between Chelsea and Roma at Stamford Bridge in London on October 18, 2017.
Image credit: Getty Images
"A lot of time, also last season. I think he has to think about his team and stop... to look at himself, not the others."
Chelsea are already without N'Golo Kante, Victor Moses (both hamstring) and Danny Drinkwater (calf).
And David Luiz suffered a calf injury against Roma which could make him doubtful for Saturday's clash with Watford, when Chelsea will be seeking to avoid three straight Premier League losses after defeats to Manchester City and Crystal Palace.
Tiemoue Bakayoko, meanwhile, played on despite a groin problem, while Conte played down concerns over captain Gary Cahill after the defender finished the game with a heavily bandaged head, saying it was "nothing serious".
Chelsea's Italian head coach Antonio Conte looks on during a UEFA Champions league group stage football match between Chelsea and Roma at Stamford Bridge in London on October 18, 2017.
Image credit: Getty Images
Chelsea had surrendered a two-goal lead, earned through strikes from David Luiz and Eden Hazard, to trail 3-2 with 20 minutes remaining.
Edin Dzeko's quick-fire double, after fellow former Manchester City man Aleksandar Kolarov's strike, looked like handing the visitors victory before Hazard headed in an equaliser.
It meant Chelsea avoided what would have been the first three-match losing streak under Conte's stewardship.
Conte, who deployed defender Luiz in midfield, admitted his tactics contributed to Chelsea being second best.
When Luiz went off for Pedro, Chelsea reverted to their usual 3-4-3 formation.
"I didn't like the type of football we did for a lot of the game, but it's right to take the responsibility for this," Conte said.
Antonio Conte, Manager of Chelsea looks on prior to the UEFA Champions League group C match between Chelsea FC and AS Roma at Stamford Bridge on October 18, 2017 in London, United Kingdom.
Image credit: Getty Images
"I tried on one hand to protect my team, to become more solid and to move our central defender into midfield. On the other hand we lost totally our style of football.
"Sometimes you have to find the right solution to try to protect your team. Sometimes it's good, sometimes it's bad. But you know very well our situation.
"It was good to draw. Roma deserved this result. I have to praise my players, because my players showed me a big effort, a big commitment tonight. Otherwise we lose the game."
Hazard rued conceding a two-goal lead, but said Chelsea can be happy to top Group C by two points from Roma ahead of the October 31 return in the Eternal City.
"When you are 2-0 up at home you must win the game," Hazard said on BT Sport 3.
"But one point is enough today after two defeats, it's not easy to bounce back against a great team but we did."
Roma boss Eusebio Di Francesco said: "We could've easily secured the three points, but we should not forget we were two goals down.
"Today we proved our character and we are definitely on the right track."
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