The Brazilian-born forward, who has scored 11 Premier League goals this season, was taken off in the 66th minute in Germany after picking up a minor leg injury.
However, speaking after Tuesday’s win, Mourinho insisted that the Brazilian should be fit for his side’s Premier League trip to Sunderland on Saturday.
Asked about Costa’s fitness, Mourinho replied: “He took a knock in his leg. He is ready for Saturday’s game.”
Tuesday’s win guaranteed Chelsea’s place in the last 16 of Europe’s elite club competition as group winners.
And Mourinho was thrilled with his side’s overall display against Roberto Di Matteo’s men.
“I don’t remember Chelsea playing in this way away from home,” he added.
“Obviously there have been some great victories away from home – with me, with other managers – but this was very impressive, very complete.
“The reality is tonight any team that played against us would find it very difficult because the players were fantastic.”
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