The Blues had gone ahead through Fernando Torres' deflected effort ten-minutes before the break, but they could not hang-on as Adrian Lopez levelled on the stroke of half-time.
Then arrived the turning point of the match came on the hour as Thibaut Courtois brilliantly saved a header from John Terry, and within a minute Ateltico had won a penalty which was clinically dispatched by Diego Costa.
The win was sealed by Arda Turan's late goal, and Mourinho admits that his side could not have given much more - but he felt they were the better side up until Atletico went ahead.
"I think until the penalty they were not the best team," he told Sky Sports.
"We had the game, we had more possession, more chances, we scored a great goal - we conceded a poor goal - we knew at set-pieces we would have chances.
"Terry had a great chance but it was a fantastic save and after that the penalty killed the game and there was only one team in it. We were trying and the players were trying everything but from that the moment the reality is that we knew we were out."
"The first half was more ours than them but finished 1-1 - which is a completely open result. Then in the second half, one minute decided everything - one minute where the Atletico goalkeeper makes an impossible save from Terry's header and in the same minute comes the penalty that kills the game. I don't know if it is - but that is the crucial minute.
"At 2-1 against Atletico it is almost impossible and after that there is only one team with high morale, knowing with half an hour to go they have the game under control and the last period of the game was gone.
"Semi-finals and important matches are made of details and this was a big detail with the save and then the penalty that left them in a great condition. But congratulations to them they are a very good side and what they are doing in the Spanish league is fantastic and I congratulate them."
The Chelsea boss was full of praise for his side, adding: "I can't be critical with the group of players who from day one tried everything.
"We had problems with injuries and suspensions and players who can't play in Champions League and with difficult moments in the Premier League too this group have had difficult moments but I am proud of them. Obviously it is disappointing to lose the second-leg of a semi-final, especially at home - but I can't criticise them for a mistake, we did everything possible for us.
"We never really had Atletico in a position where we had an advantage where they had to chase a game, maybe ten minutes, five minutes. ut that is football and we have to accept that."
Mourinho insists he is pleased with how Chelsea have performed this season but is predicting improvements next season.
"Next season will be better than this season.
"We are discussing the Premier League with two matches to go which is an improvement from previous seasons and to arrive in the Champions League after being knocked out in group stage is a step up.
"Hopefully we can bring in a couple of players to improve the team, but I am happy with the players and what they have done - today we did not have happiness in our team, but until the penalty they were not the better team but I congratulate them."
Asked about Thibaut Courtois - on loan from Chelsea and who pulled off the great save from Terry - Mourinho would not speak, and simply said: "No, he is Atletico's."