With the contest tied at 1-1 and Atletico heading through on away goals Chelsea had a chance to go in front for a second time, but Thibaut Courtois, playing against his parent club, saved a John Terry header.
Atletico advanced down the other end and substitute Samuel Eto'o tripped Diego Costa, with the striker coveted by Chelsea converting the penalty to take his side 2-1 up and effectively end the contest and send the Primera Division leaders through to the May 24 final in Lisbon.
"In one minute two actions decided the game," Mourinho said.
"Atletico's goalkeeper makes an impossible save from John Terry's header and instead of 2-1 to Chelsea, a few seconds later a penalty.
"The save is amazing and the penalty is a penalty.
"After that, there was only one team on the pitch. We had immediately 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."
UEFA had intervened to allow Courtois to play against Chelsea amid reports of a contractual clause, but Mourinho had no animosity over the situation regarding the Belgian, who was playing his first game at Stamford Bridge on his third successive season on loan in Spain.
Mourinho added: "No, no, he's the Atletico goalkeeper, playing for Atletico and he did his job."
Chelsea's defence, with captain John Terry back sooner than expected after an ankle injury sustained in the first leg, was less impressive than earlier this season, but the Blues boss refused to attribute blame.
"I'm not going in that direction now," Mourinho said.
"I said yesterday in the press conference every one of my players was ready.
"Every one of my players tried the maximum. Eto'o was here today almost without one training session, Oscar on the bench and he was injured.
"We had so many problems, but the players gave everything. I'm happy with them.
"They can go home sad, obviously, but with clean faces. They did their work well.
"They lost, but they lost against a very good team. And that's football."
Unless there is a remarkable final twist in the Premier League title race, Mourinho is poised to finish without a trophy for a second successive season for the first time.
Assessing his first season back at Stamford Bridge ahead of the closing Premier League matches with Norwich and Cardiff, Mourinho said he and his players clung to a dream which disappeared.
"We are realistic, but at the same time we are optimistic," he said.
"When things go in a certain direction, there is a moment where you dream and you think that things are possible, even if things are not.
"And because we did well in the Champions League and in the Premier League, there was a moment where we felt we could do it.
"In the Premier League it was the match against Aston Villa that made me believe that we had no chance to be champions.
"After that we build again the momentum and we were waiting for the Liverpool match to be the title match, but we had another surprise against Sunderland.
"In the Champions League, it's the same. We knew that teams had more potential than us and were more ready than us to win the competition, but because you go step by step and beat Paris St-Germain after a 3-1 defeat, you build your dream.
"And today, I think it was proved that we had our chances.
"Until minute 61 we were completely in the game. And 2-1 for Chelsea, or 2-1 for Atletico.
"That moment was crucial and, from that moment, the game was over."
Fernando Torres scored against his former club to put Chelsea in front, but Adrian swiftly equalised and it was that period before the interval which Atletico boss Diego Simeone felt was decisive.
"The reaction to the first goal was crucial," Simeone said.
"At 2-1 it settled the game and from then on we controlled the game."
Simeone believes the introduction of Eto'o helped Atletico.
He said: "We benefited greatly from that, in the fact they had Eto'o, Torres and (Eden) Hazard, because they played in the high line which left us more space to control the game."
Real await in the final.
"We know each other very well," Simeone added.
"They're a very powerful club used to those big European nights.
"It's been many years for us as a club, so it'll be a new experience. But we're keen and excited to play well."