Defending United's cautious tactics in last weekend's draw at Liverpool and Wednesday's 1-0 win over Benfica, Mourinho made it clear he had opted for a conservative approach because his side are missing key players.
But Mourinho insisted that wasn't making excuses, a charge he believes others are guilty of in the Premier League.
Chelsea boss Conte has repeatedly mentioned his team's injury problems during their current winless run, which extended to three matches after they were held to a 3-3 draw by Roma on Wednesday.
Conte is without N'Golo Kante, Victor Moses and Danny Drinkwater, while Alvaro Morata has just returned to fitness.
"I never speak about injuries. Other managers, they cry, they cry, they cry when a player is injured," Mourinho said after the win in Benfica.
"If I wanted to moan and others I could cry like the others for five minutes; Ibrahimovic, Fellaini, Pogba, Rojo."
Told of Mourinho's comments by a journalist, Conte asked if they were aimed at him.
When the response was yes, Conte visibly bristled before angrily telling former Chelsea boss Mourinho to mind his own business.
"If this is for me my answer is this -- he has to think of his team and look at himself not the others," Conte said.
"A lot of times Mourinho has to see what happened in Chelsea. Also last season. He has to look at his team."