The German side gained revenge for their 2012 Champions League final defeat by Chelsea when they beat the Premier League club 5-4 on penalties after a thrilling match ended 2-2 at the end of extra-time.
Bayern dominated possession and had a slew of chances after Chelsea were reduced to 10 men following Brazil midfielder Ramires's sending-off in the 85th minute for a second bookable offence.
"I'm disappointed because in my opinion, and I can have an opinion, I won't be punished by my opinion, is that the best team lost," Mourniho said. "That is what happens sometimes in football."
The Portuguese coach also questioned the length of added time but saved most of his fire for the yellow card, suggesting that a referee in England would not have done the same.
He then ticked off a list of big matches his teams have played with only 10 men, including games against Barcelona and a Champions League final when he was coach at Inter Milan.
"There is a very important rule, and that is the passion for football," he said. "And if you are in love with football, you don't kill a final with the second yellow card like this.
"This with English referees, with people who love the game, with people who love to communicate with the players, with people who love to coach the players, this with a good English referee, (he) stops the game, he tells Ramires 'you did not hurt anybody, but you could', tells the Munich players 'don't dive, don't provoke, play a fair game', and the game would be level 11 against 11."
Mourinho said it was not a new situation for him.
"I was in Chelsea and I played two or three times with 10 men against Barcelona. I came to Inter and I played Champions League semi-final for one hour with 10 men against Barcelona," he said.
"I go to Real Madrid, I play again Champions League semi final with 10 men. I come back to Chelsea, I play Super Cup final with 10 men again and go analyse the actions and take your conclusion. I'm unlucky, I'm just that."
Bayern coach Pep Guardiola gave a different account of the game and declined to comment on the red card.
"The best team won today," he said. "We had huge opportunities to score because we were very good on the attacking front.
"It is normal, he can say his team deserved better than what happened. I too have my opinion."
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