Mourinho, speaking after United's 1-0 win at Benfica 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 a 3-3 draw which extended Chelsea's winless run to three games, Conte retaliated.
"A lot of time Mourinho has to see what happens at Chelsea," Conte said.
"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 had surrendered a two-goal lead, through strikes from 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 a third straight loss for the first time 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.
"Sometimes you have to find the right solution to try to protect your team. Sometimes it's good, sometimes it's bad."
Chelsea top Group C by two points from Roma ahead of the October 31 return in the Eternal City. United visit Stamford Bridge in the same week, on November 5.
Mourinho was sacked by Chelsea for a second time in December 2015, seven months after winning the Premier League title.
And Conte revived the Blues to claim the title in his first campaign as boss.
Hazard rued conceding a two-goal lead, but says Chelsea can be content with avoiding defeat.
"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."