Diego Costa's first-half equaliser cancelled out Cristiano Ronaldo's early header at the Bernabeu, before Miranda's extra-time goal delivered Atletico's first victory over Real for 14 years.
Madrid's frustration told and, with Mourinho having been sent from the technical area during normal time, Ronaldo saw red in the 114th minute for kicking out at Atletico captain Gabi - who was himself dismissed in the frantic final minutes for a second bookable offence.
The defeat rounded off a trophyless campaign for Real and Mourinho, disregarding the Spanish Supercopa, prompting the Portuguese to declare: "This is the worst season of my life."
Mourinho has been widely tipped to return to Chelsea but reiterated that he would not make any announcement about his future until he has a meeting with the club president Florentino Perez at the end of the season.
He said: "I have a contract here for three more years. I still haven't sat down with the president to talk about the future."
On rumours touting Paris St Germain coach Carlo Ancelotti as his potential replacement, he continued: "I think it's normal that they talk about Ancelotti. That's normal, if I go to Chelsea, or here or there... that's normal for people to talk abut that. We will make it official when me and the president sit down and decide what to do.
"That's the way it should be. There are still two games in the league to play. We have to play the league and respect the other teams we are playing - Real Sociedad and Osasuna - who still have objectives, like qualifying for the Champions League and avoiding relegation."
If Mourinho does leave the Spanish capital this summer, he will have won just three trophies in his three-year tenure at the club: the 2011 Copa del Rey, the 2011/12 La Liga title and the Spanish Supercopa - traditional season curtain raiser - this term.
He defended his record in his first two years in charge of Los Blancos, but admitted he had "failed" this year.
"I failed this season," he said. "I think it's normal in my first season that we won the cup - a cup the club had not won in 20 years - reached the semi-final of the Champions League, fought virtually to the end for a league that they (Barcelona) won year after year... the team everyone said was the best in the world.
"My second season was not a failure because we won the league against the best team in the world and got to the Champions League semi-final and lost on penalties, and I'm sorry, because I can't take penalties.
"The third season is a failure. This is the worst season of my life. For many coaches it would be good, but for me it's terrible. I had never finished a season without one of the important trophies. The Supercopa does not satisfy me."
Mourinho also praised goalkeeper Thibaut Courtois - on loan at Atletico from Chelsea - who made two outstanding saves in extra time to deny Gonzalo Higuain and Mesut Ozil, but also cursed his team's luck, as Ronaldo, Ozil and Karim Benzema all hit the woodwork, while Ozil had a shot blocked on the line by Atletico defender Juanfran.
"He is a fantastic young goalkeeper with great potential and I think his club has to decide his future and that club is Chelsea," he said.
"He made fantastic saves but they were not just fantastic saves - Saint Mary must have been behind the goal. Three shots off the post is too much."
Mourinho refusd to comment on the second-half incident which saw him sent to the stands.
Atletico coach Diego Simeone declared that his team should be an inspiration to less fortunate people around the world after their triumph.
He said: "We are the hope for society, a reference for people suffering, who are not enjoying the best of times. If you work hard, your moment will come."
Despite having had to rely on the outstanding Courtois and the woodwork for the victory, the Argentinian insisted his team were worthy winners.
"It was an incredible game. We had the luck that you need to become champions, but what these players have done in the last year and a half is incredible. I am lost for words," he said after guiding Los Rojiblancos to their first win over Real since 1999.
"We managed to win the most important game of all. The team played with all their hearts and showed an enormous will to win. We admitted in the build-up to the game that they were better than us, but we played better than them and that made us stronger.
"After losing 2-0 here in the league (in December) I told the players that I wished that destiny would give us the chance to play against them in a final.
"It has been very difficult for us to win a derby, but the support of the fans tonight made us feel like we were playing at home.
"The fans must be very proud of the team they have. I think the fans would have accepted this moment 14 years ago - to finally beat Madrid in their home, in a final, coming back from being 1-0 down."