The Brazilian was enthused by the doggedness and determination Diego Simeone's men showed in extending their advantage at the summit of the Primera Division to six points
The Rojiblancos looked set to squander their chance to move six points clear at the top of the Primera Division when David Villa missed a penalty shortly after half-time in a game at the Vicente Calderon in which the visitors looked more than capable of causing an upset.
However, Atletico finally made the breakthrough when Miranda headed home a Jose Sosa corner with 18 minutes to go and Diego Costa's injury-time penalty belatedly allowed the home fans to relax and start looking forward to Tuesday's Champions League semi-final first-leg tie against Chelsea.
"This was an important win," the Brazilian centre-half told Canal+. "The team was good and we must carry on like this.
"We've got four finals left now and the team knows how to suffer, when we have to suffer.
"Now, though, we must rest and think about the game against Chelsea."
Miranda, who scored the winner in last year's Copa del Rey final win over city rivals Real, revealed that his goal from Sosa's corner was a rehearsed routine.
"It's a move we've trained for, one we've worked on a lot," the defender claimed. "We have good takers and plenty of quality players at set-pieces."