Costa picked up his fifth yellow card of the season during the goalless draw at Sunderland on Saturday.
The Spain striker may have been fortunate not to receive a red card for the challenge which brought his latest booking, having seemingly elbowed Sunderland defender Wes Brown.
Either way, he will miss Wednesday's home clash with Mauricio Pochettino's side - which would seemingly represent a blow given he leads the Chelsea scoring charts.
Mourinho, who claimed not to see Costa's challenge with Brown, is confident either Loic Remy or Didier Drogba can step up in his place.
He said: "We don't cry about injured or suspended players. If he is suspended, he is suspended. We have Drogba and Remy.
"We are top of the league and we have another match on Wednesday."
When it was suggested Costa was 'feisty' and may have to be careful in the Premier League, Mourinho replied: "Why do you always talk about Diego? I don't think so."
Mourinho conceded he was not happy with a point at the Stadium of Light, but did not criticise his players' performance.
He added: "It was difficult. They [Sunderland] had spent one week preparing for the match and had a clear strategy.
"Many people criticise defensive teams. I don't do that because you have to do it well and they did.
"We always tried to play and move the ball but they defended very, very well. I praise them for their success in getting a clean sheet.
"I have no negative words to my players because they tried everything and were not successful.
"I thought it was a fair result. We are not happy with a point but we have to be mature and experienced enough to know every match is difficult in this league."
Chelsea remain unbeaten in the Premier League this season, having taken 33 points from 13 matches.
