Costa came off clutching his side in the 33rd minute of the fourth-round tie at the Britannia Stadium, which the Blues lost 5-4 on penalties following a 1-1 draw after extra time.
Asked in his post-match press conference what the situation was with Costa, Mourinho replied: “He is in the hospital – I don’t know.”
When then asked if the Spain international would be a doubt for Saturday’s Barclays Premier League home clash with Liverpool, Mourinho said again: “I don’t know.”
Costa was substituted shortly after being sandwiched between Ryan Shawcross and Charlie Adam in a tackle and then trying to muscle his way towards a Willian cross that Stoke goalkeeper Jack Butland punched away.
And Mourinho added when asked how the injury had happened: “I think he punched himself.”