The Belgian - who is on loan from the Blues - made a fine stop to deny John Terry before Diego Costa's penalty, which the Portuguese coach says decided the tie
Fernando Torres opened the scoring for the Blues at Stamford Bridge but goals from Adrian Lopez, Diego Costa and Arda Turan secured victory for Diego Simeone's side and sets up a final against neighbours Real Madrid in Lisbon.
Courtois - currently on loan at Atletico from Chelsea - made a fine stop to deny John Terry moments before Costa's decisive penalty kick, and Mourinho believes that crucial minute decided the tie.
"The game until a certain minute was very, very, very equal," he told Sky Sports.
"The first half was more ours than them but finished with a 1-1 which is a completely open result. And in the second half one minute decide everything.
"A minute where Atletico goalkeeper makes an impossible save for John Terry's header. And in the second minute it's a penalty that kills the game. I don't know if it's a penalty; I'm too far [away].
"That was the crucial minute. After that, 2-1 against Atletico is almost impossible. And after that there was only one team - a team with high morale knowing that with half an hour to go they have the game and the result."
There was speculation before the semi-final games that Courtois would be unable to play against his parent club due to a clause regarding a potential fee agreed between the sides, but Uefa announced on 11 April that any such clause in the Belgian’s contract with Chelsea was "null, void and unenforceable" during a Champions League fixture.
Atletico now have the opportunity to complete a Champions League and La Liga double, and will face city rivals Real in the final after Carlo Ancelotti's men demolished Bayern Munich 5-0 on aggregate on Tuesday.