r City.
Chelsea were held to a 1-1 draw by Schalke, who they twice beat 3-0 last term, after Cesc Fabregas' 11th-minute strike was cancelled out by Klaas-Jan Huntelaar.
Costa, who has scored seven goals in his first four Premier League games following his £32million summer move from Atletico Madrid, came off the bench but was unable to find a winner.
"Costa has a problem," said Mourinho of the striker, who scored a hat-trick in Saturday's defeat of Swansea.
"If he has one week to let the muscle recover he can start a game
Playing on Saturday, three days is not enough for him to recover.
"It was not to protect for the game Sunday (at Manchester City) it was because today he was not in condition to start the game."
Costa limped out of last season's Champions League final with Atletico with a hamstring problem and the injury recurred while on international duty earlier this month with Spain.
"He played here one match and he was perfect," Mourinho said.
"He went to the national team and after the game against France he came back to us injured.
"He came to us (from Atletico) and he was completely fine
He had a problem again in the national team, not with us.
"Now we have the problem and now we have to resolve the problem the best we can.
"Today he was not in condition to play
Sunday we believe he is.
"Next week against Bolton (in the Capital One Cup) for sure he isn't
We have to manage the situation until the moment he's completely fine.
"If today he starts the game, for sure he cannot play on Sunday
We have to go step by step."
The Germans were severely depleted by injury and reeling from their worst Bundesliga start in more than 40 years
It appeared Chelsea would run amok after a scintillating start, with Eden Hazard to the fore.
Instead Chelsea failed to take their chances, with Didier Drogba among those culpable, and Mourinho was left to rue defensive lapses as Schalke equalised and held on for a point.
It appeared Huntelaar had fouled Fabregas in the build-up to the goal - the Spain midfielder had appeared to have tackled Max Meyer late in the move which led to his goal - but Mourinho had no complaints.
"From my position I can't say that (it was a foul)," Mourinho added.
"They scored 1-1 in a counter-attack situation
We made two mistakes.
"One was not to make a foul immediately when they recovered the ball and we had a chance for that.
"The other one was the fact I told my players 20 times Draxler wants to come inside for his right foot and in a situation inside the box we have to press his right foot
It was also a mistake in the box.
"After that situation only one team tried to win and only one team had so many chances to win the game in a short period of time.
"In the last 15 minutes Remy could score, John Terry could score, Hazard could score.
"We had so many great situations
Again, that's football
To defend like they did is also football.
"A good point for them
Not a fantastic point for us, but a point."
Drogba deputised for Costa on his first Champions League appearance for Chelsea since scoring the decisive penalty in the 2012 European Cup win.
The Ivory Coast striker was unable to convert passes from Willian and Hazard, but Mourinho refused to be critical of the 36-year-old.
"He had a positive game," Mourinho said.
"I'm not disappointed with the striker because of one inch, he scores a goal or doesn't score a goal.
"I am happy with what he did
If he scores that goal in this moment we're speaking about 2-0, not 1-1.
"We had very good chances to score the 2-0 and we didn't.
"After the 1-1 we had a fantastic reaction and chances to win the game, but that's football, that's Champions League, that's normal.
"Congratulations to them because they got their objective
Yes a little bit of frustration for us, because we did everything to win and we couldn't."
Schalke boss Jens Keller was thrilled with his side's display.
He said: "I'm very, very proud of what my team did here against such a top team.
"Tactically we did exactly how we had planned
We were aggressive, we played right into space.
"We had really good tempo with Draxler and Sidney Sam.
"I'm absolutely delighted with the performance we gave here today."
Source : PA
Source: PA