Costa appeared to hurt himself in a collision with and after initially playing on, he went off in the 33rd minute, with Loic Remy taking his place.
"He's in the hospital," Mourinho told his post-match press conference at the Britannia Stadium. Asked how Costa had sustained the injury, he replied: "I don't know. I think he punched himself."
Chelsea lost 5-4 on penalties, with Butland saving the decisive spot-kick from Eden Hazard after the game had finished 1-1 in normal time.
Costa, 27, was Chelsea's top scorer last season with 21 goals in his first campaign after signing from Atletico Madrid, but has found the net only three times in all competitions this season.
