Both strikers are both expected to be unavailable when Chelsea head to Old Trafford on Sunday.
Costa has missed Chelsea's last two games due to hamstring trouble, while Remy suffered a groin injury in the act of opening the scoring as Mourinho's men trounced Maribor 6-0 on Tuesday in the UEFA Champions League.
Didier Drogba, who was also on target against Maribor to register his first goal since returning to Stamford Bridge, could now lead the line against United and Mourinho is remaining relaxed.
"I'm not worried. When a player is injured, play another one," said the Portuguese.
"[Wednesday] is a day off and the doctor is forbidden to call me to speak about injuries. I don't want to speak about injuries, Man United. I don't want to know.
"We don't cry on injuries. It's our philosophy, we don't cry. We just think one injury means an opportunity for somebody else.
"We cannot hide. In this moment we have some problems with players that are not available to play.
"We will prepare [for] the game Thursday, Friday, Saturday to try to be at our best possible level against an opponent which we respect very, very much."
Mourinho was pleased to see the 36-year-old Drogba complete the vast majority of Tuesday's match after replacing the injured Remy.
"I spoke with him yesterday and we spoke about [him playing] 30 [minutes]. Circumstances. He had to go on." he said.
"He was comfortable to play 75 minutes. It was very, very important for Didier. The best thing for a player to improve his condition is to play."
