The Portuguese played down suggestions of a breakdown in relations with Costa after the bib incident which followed a touch-line spat during Tuesday's Champions League win over Maccabi Tel Aviv.
"Diego is very privileged because he was the last one to be on the bench," Mourinho told reporters after the game.
"The captain (John Terry) has been on the bench, so have (Branislav) Ivanovic, (Gary) Cahill the vice-captain of England, (Cesc) Fabregas, Pedro, Oscar, (Eden) Hazard, the player of the season.
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"So he is privileged I kept him in the team for all these matches.
"Physically Diego is fine. He is working well every day and his mood is positive. He was ready to play when we he went to warm up. I have a good relationship with him."
Costa, who scored 20 goals in his first season with Chelsea, has found the back of the net just three times in 11 league appearances this campaign and has admitted he was overweight when he returned to pre-season training.
Champions Chelsea have made a dismal start to their title defence, losing seven of their first 12 league games to sit five points above the relegation zone, and Mourinho said it had been a learning experience.
"I learned how to live without the happiness of winning matches," he said.
"I learned how to motivate myself without the target of being champion, which is not easy for somebody that always had the happiness of winning matches very regularly and somebody who always played - with the exception of (Portuguese side) Uniao de Lleiria - with the objective and the target to be champion."
(Reporting by Shravanth Vijayakumar in Bengaluru. Editing by Patrick Johnston)
