The Spanish international joined the Blues from Atletico Madrid during the summer transfer window for a fee of £32m, scoring seven goals in his first four Premier League games.
However, Costa had to make do with a place among the substitutes for last night's 1-1 draw against Schalke, with Mourinho revealing after the game that his star striker has not yet shaken off a hamstring injury which he recently picked up on international duty.
"Costa has a problem," the 51-year-old coach told Sky Sports News. "He came to us [from Atletico] and he was completely fine. He had a problem again in the national team, not with us.
"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, it was because he was not in condition to start the game.
"Now we have the problem and now we have to resolve the problem the best we can. 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."
Costa scored 43 goals in 94 appearances for Atletico before making the move to Stamford Bridge.