Mourinho, looking down in the dumps after Chelsea could only draw 1-1 with Schalke 04 in their opening Champions League Group G match on Wednesday, started with returning veteran striker Didier Drogba in attack with Costa on the bench against the Germans.
The Brazil-born Spain international, who cost Chelsea 32 million pounds when he joined from Atletico Madrid in the summer, replaced Drogba in the 74th minute, but could not keep up his remarkable scoring record which includes four goals in pre-season and seven in the League including his hat-trick against Swansea City on Saturday.
Mourinho said Costa's injury is not connected to one he suffered towards the end of last season and which restricted him to just the first nine minutes when he played for Atletico against Real Madrid in last season's Champions League final.
He did recover from that to play for Spain in the World Cup and Mourinho added: "When he came to us he was completely fine. He got the problem with the national team."
Costa picked up the injury in Spain's 1-0 defeat to France on Sept. 4 and Mourinho said he could not play more than one match a week for the time being.
"If he has one week to let the muscle recover he can start. He played on Saturday and was not in condition to start the game today."
Costa scored the last time he played in a Champions League match at Stamford Bridge - when he banged home a penalty in Atletico's 3-1 win over Chelsea in last season's semi-final - but failed to hit the target during the later stages of the game against Schalke as Chelsea sought the winner.
"It was not to protect Costa for the game against Manchester City on Sunday, it was because he was not in condition to start the game," Mourinho said.
"Playing on Saturday, three days is not enough for him to recover. He will play against City but he cannot play against Bolton (in the League Cup) next week, that's for sure."
Drogba, back at Chelsea after two years away playing in China and Turkey, was playing in his first Champions League match for the club since scoring the decisive penalty in the 2012 final shootout against Bayern Munich.
He had two good chances to score but fired narrowly wide and then blazed a chance over the bar in the second half.
Chelsea dominated much of the match and took the lead when Cesc Fabregas scored his first goal for the club in the 11th minute but Chelsea failed to capitalise on their superiority and allowed Schalke to escape with a point after Klaas-Jan Huntelaar equalised in the 62nd minute.
(Editing by Amlan Chakraborty)
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