Belgian international Courtois, 21, has been on loan at Atletico from Chelsea since 2011 and he produced a save in Wednesday's second leg at Stamford Bridge that Mourinho identified as the key moment in the tie.
With Atletico ahead on away goals after Adrian Lopez had cancelled out Fernando Torres's 36th-minute opener for Chelsea, Courtois plunged to his left to block a header from home skipper John Terry.
Moments later Diego Costa put Atletico 2-1 up from the penalty spot after he had been fouled by Samuel Eto'o and a late Arda Turan effort completed a 3-1 victory that set up a showdown with city rivals Real Madrid in the final in Lisbon on 24 May.
"The difference was one minute in the second half, where the Atletico goalkeeper makes an impossible save from John Terry's header," said Mourinho, whose side had drawn 0-0 in last week's first leg. "Instead of 2-1 for Chelsea, a few seconds later, there is a penalty, which I'm happy people tell me was a penalty, and they scored the 2-1.
"That minute was crucial. After that, they had complete control and we had the feeling the game was lost. They had the feeling the game was in their hands and after that they were very solid, very mature, a real team. I knew before they were a real team, and I congratulate them."
Courtois was making his first appearance at Stamford Bridge, but Mourinho said that he was not frustrated by the knowledge that Chelsea had effectively been denied by one of their own players. "No, no, no," he said. "He's the Atletico goalkeeper, he plays for Atletico, and he did his job."
Atletico coach Diego Simeone, meanwhile, was evasive when asked if he would like to keep Courtois at the Vicente Calderon for a fourth season.
"I'm just experiencing this moment, trying to relish this moment," he said. "I'm sure in the future the directors will decide what's best for this young lad and whether he will stay at the club or not."
Mourinho optimistic for future
Simeone has worked wonders in his two and a half years at Atletico, guiding the club from 10th place in La Liga to their first European Cup final since 1974 and to the brink of a first league title since 1996.
Mourinho, in contrast, is less than a year into his second stint at Chelsea and he said that it would take time for him to produce the same results.
Asked for the difference between the two teams, he replied: "The difference between one year and three. It's a big difference. One year is one year, three years are three years. I think Atletico are a very, very good side, very adapted to the ideas of their manager. It looks like every player fits his idea of how to play."
Chelsea are currently two points below Premier League leaders Liverpool with two games to play, but Mourinho does not believe that it is realistic for his team to aim for trophies at this stage of their development. "We are realistic, but at the same time we are optimistic," he said.
"When things go in a certain direction, there's a moment where you dream and you think things are possible, even if things are not so realistic. Because we did well in the Champions League and in the Premier League, there was a moment where we felt we could do it."
He added: "Next season will be better than this season. That's our objective, the objective of everybody.
"Our young players will be better, hopefully we will have a couple of players to improve our team, and we will try to do better next season."