Read: Read: Mourinho bites tongue over Courtois red card
The injury had ruled Costa out of Chelsea's Community Shield defeat to Arsenal and their last pre-season game against Fiorentina.
"He did very well and in the second half it was very difficult because there was a big distance (between him and his teammates), we had one player less and it was a great effort," Mourinho said.
"Even so, I was not expecting him to resist for 90 minutes but because we wanted to try to collect a goal we went with him until the end and it was very important for us that he played for 90 minutes with such a physical performance.
"He's very happy with the reaction of his body after such a difficult game," the Portuguese manager added.
The 52-year-old Mourinho said Chelsea do not miss goalkeeper Petr Cech and he was sure his side would cope well without the suspended Thibaut Courtois when they visit Manchester City on Sunday.
Read: London Bridge is falling down : Arsenal Cech themselves, wreck themselves at Emirates
Mourinho was not keen on allowing the 33-year-old Cech to join London rivals Arsenal after 11 successful years with the champions, but the manager insists he is happy with the goalkeeping options at his disposal.
"We don't miss Petr," Mourinho was quoted as saying by the British media.
"We've got a good keeper, the problem with Petr is not that we miss him because we have two excellent keepers.
"The problem with Petr is that an opponent is better than before."
Cech opted to move to Arsenal after finding himself playing second fiddle to Belgian international Courtois, who Chelsea recalled from loan at Atletico Madrid last season.
Chelsea bought Stoke City keeper Asmir Begovic as a back-up to Courtois following Cech's transfer.
"Thibaut and Asmir are two fantastic keepers. My club did very well by getting a keeper on time and not on the August 31," Mourinho added.
Courtois is banned for the match at the Etihad Stadium after he was sent off against Swansea for a foul on striker Bafetimbi Gomis, which earned their opponents a penalty and allowed them to draw the game 2-2.
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