Mourinho criticised other coaches who "cry" over absent players, in the wake of Marcus Rashford picking up a knee injury in the Champions League victory over Benfica.
United are also without Zlatan Ibrahimovic, Marouane Fellaini, Paul Pogba and Marcos Rojo due to long-term fitness complaints, but Mourinho has refused to detail their respective prognosis.
Conte meanwhile has recently lost three players to injury, with Victor Moses joining N'Golo Kante and summer signing Danny Drinkwater on the sidelines after the defeat to Crystal Palace.
That injury list is set to grow after the 3-3 draw with AS Roma at Stamford Bridge. Eden Hazard scored twice to rescue a point for the Blues but a series of injuries overshadowed a point which keeps the 2012 on course to qualify for the last 16.
David Luiz was replaced by Pedro after 57 minutes after picking up a calf problem in the first half; Tiemoue Bakayoko played the whole game with a groin issue; while Gary Cahill needed bandaging to treat a facial knock.
The various injuries could leave Conte without six players for the visit of Watford this Saturday [21 October], though the Italian was more focused on sending a barb to Mourinho, who had taunted the ex-Juventus boss and his colleagues during his own post-match press conference.
"Do you think that it was for me? I think that he has to think about his team," said Conte. "Stop, look at himself, not the others.
"I think a lot of the time Mourinho has to see what happens at Chelsea. Also last season. If it is for me, my answer is this. If this not for me my answer is not for him."
The exchange comes just 17 days before Chelsea host United in the Premier League - a fixture which now has all the ingredients to be an explosive affair, coming on 5 November, Bonfire Night. In the reverse fixture last term, Chelsea ran out 4-0 winners in Mourinho's first game against the club he spent two spells at as a manager, since taking over at Old Trafford.
Conte's focus for now will be on getting some of his key players fit before United come knocking. The reigning English champions host Watford and then Everton in the Caraboa Cup, before trips to AFC Bournemouth and Roma prior to facing one of the favourites to take their league crown.
Luiz was substituted after clearly picking up a leg injury in the first 45 minutes, but complained over being withdrawn when he was finally replaced by Pedro. Conte says he was informed over the Brazilian and Bakayoko's fitness problems at half time but was forced to persist with them given his lack of options.
"After the first half the doctor told me that David Luiz had a pain in his calf, the same for Bakayoko in his groin," he added. "I think it was a good decision to try and protect him because in this moment it is very important to protect the players. I change the system and I prefer to change.
"I must protect players. We had three important players out; Kante, Drinkwater and Moses. This situation gives us problems but I am not looking for excuses. [Cahill] has an injury, nothing serious. It is a knock. The doctors are looking at it."