The striker, a surprise name in Atletico's XI considering his recent fitness woes, did not last 10 minutes against Real Madrid before being brought off
The Spain international has been struggling with a hamstring problem recently and was also substituted off very early into Atletico's final game of the Liga season at Barcelona.
He was a major doubt to feature in Lisbon against Real Madrid but, after it emerged that he was undergoing horse placenta treatment in a boost to return to fitness, he was surprisingly named in Diego Simeone's starting XI for Saturday's final.
However, Adrian was brought on for the for the Brazilian-born attacker when it was clear that Costa could no longer play on, with less than 10 minutes played at Estadio da Luz.
Costa has scored 36 goals this season for Simeone's men, with eight strikes in eight appearances in the Champions League.
The 25-year-old's goals played a large part in their Liga triumph in 2013-14, topping rivals Real and Barcelona, and he is widely tipped to make a mega-money move to Chelsea this summer following his exceptional form.