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 Saint-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 Primera Division 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.