Simeone – who last Saturday led Atletico to their first La Liga title since 1996 – was sent off in the dying stages of extra time after running onto the field to confront Real Madrid players shortly after Cristiano Ronaldo completed the scoring in his side's 4-1 victory in the all-Spanish final.
The fiery Argentinian appeared to exchange angry words with Real defender Raphael Varane after watching his side capitulate late on in Lisbon.
Carlo Ancelotti's men dug deep, though, and finally saw a significant spell of sustained pressure rewarded when Sergio Ramos headed in a corner to force an additional 30 minutes.
After the first period of extra time ended goalless and Simeone confronted referee Bjorn Kuipers, Atletico, visibly struggling, folded, as Bale – scorer of Real's extra-time winner in last month's Copa del Rey final – popped up at the far post to nod his side in front in the 110th minute.
Marcelo then rifled in a third with two minutes to play before Ronaldo's penalty sparked shameful scenes from Simeone.
Victory means Ancelotti has now won the trophy as coach on three occasions, making him the most successful manager in the competition's history, while Atletico were left to rue another late goal in European football's showpiece. The club's only other final appearance, in 1974, saw Bayern Munich force a replay – which they won 4-0 - with a 120th-minute goal.
Simeone's experiment to start Costa – who travelled to Serbia for specialist treatment on a niggling hamstring injury in the build-up – quickly backfired, though, as the striker limped off in the ninth minute and was replaced by Adrian Lopez.
And Bale's missed chance proved costly in the 36th minute as Godin gave Atletico the lead against the run of play.
Real failed to clear a corner and Juanfran's header back into the box caught them napping, meaning goalkeeper Iker Casillas had to come storming off his line.
Ancelotti's men kept pressing as Isco missed the target with a long-range effort and although Atletico were still a threat on the counter-attack, they were forced back as Real ramped up the pressure in the last 20 minutes.
Desperate blocks were the order of the day as far as Atletico were concerned, but Real's perseverance eventually paid off as Ramos superbly planted a header in the bottom-left corner from Luka Modric's corner to force extra time.
And the added half-hour proved crucial as Real took the lead with 10 minutes remaining through Bale, who raced to the far post after Angel di Maria's shot was partially saved to head in.
