Striker Loic Remy (groin) and midfielder John Obi Mikel (foot) are out, but Ramires is back from a groin problem to bolster the midfield.
Branislav Ivanovic is available following his suspension for his dismissal at Manchester United, but fellow full-back Cesar Azpilicueta is banned for the last of three games following his sending off at Crystal Palace.
The saving grace has been the form of 36-year-old Didier Drogba, who has scored in three successive matches against Maribor, Manchester United and Shrewsbury.
Those goals were Drogba's first since his return to Stamford Bridge following a two-year absence after eight years and 157 goals.
"For such a legend in this club, it's a difficult decision to take," Mourinho added.
"We took it together: owner, board, me, him, all of us together.
"To be important you don't need at the age of 36 to play 90 minutes of 50 matches.
"To be important you need to be there when the team needs you to be there.
"He was fantastic for us in the last week when we were in real trouble, without Diego and without Remy.
"And doing something that nobody should do, which is to play two 90 minutes of football with 48 hours difference
He managed to do that in an absolutely fantastic way."
Given Drogba's form, it may be Mourinho retains him in his starting XI, even with Costa available.
"Fantastic problem for me," Mourinho added.
"The perfect problem is when Remy is back
That's the perfect problem, to have all three."
Midfielder John Obi Mikel (foot) is also out of the QPR contest, but Ramires is back from a groin problem.
Branislav Ivanovic is available following his suspension for his dismissal at Old Trafford, but fellow full-back Cesar Azpilicueta is banned for the last of three games following his dismissal at Crystal Palace.
QPR have two wins this season - in August versus Sunderland and last Monday against Aston Villa - and manager Harry Redknapp has been under pressure.
Mourinho is supportive of Redknapp.
"I don't think he's under pressure," the Blues boss said.
"I'm happy that his boss (QPR chairman Tony Fernandes) came out and in difficult moments, not in an easy moment, and told the football country that he trusts Harry and he's the man for now, he's the man for the future.
"Harry is perfectly calm and steady and he knows that his place doesn't depend on results."
It is the first time Mourinho has met QPR as Chelsea boss, but he is not underestimating Redknapp's men.
"In my years here they were always in the Championship," Mourinho said.
"Everybody knows that London is a special place because of derbies
You play eight or 10 derbies (in a season).
"The London teams have more difficulties than others, because a derby is always a derby.
"What they did before is not important for me
What they can do tomorrow is more important for me.
"I think I know what I can expect from them
It will be a difficult game for us."
Redknapp could call upon QPR's misfit midfielder Adel Taarabt after the duo patched up their public spat.
The Rangers boss has refused to rule out pitching the Morocco playmaker back into action with Jordon Mutch and Joey Barton not back in full training until next week following hamstring problems.
Taarabt has apologised to Redknapp after biting back when his manager branded him "about three stone overweight".
Redknapp has admitted he must use Bobby Zamora sparingly to control the striker's chronic hip problems.
Rangers boss Redknapp hailed the 33-year-old's resolve for playing through the pain, but conceded the former Tottenham forward cannot last a full 90 minutes.
Zamora has battled rumbling hip complaints for almost two years, but Redknapp said QPR are fighting to keep him in action as long as possible.
"Bobby has been very important for us," said Redknapp.
"After about 60 to 65 minutes he has to come off, but when he's on the pitch he has been outstanding.
"We were bringing him off the bench to start with, but we've reversed it and started him recently.
"He's been captain and great in the dressing room, I couldn't be more pleased with Bobby.
"He's got his hip but he manages it and when he plays he's been great and his attitude has been first class."
Source : PA