Diego Simeone's men climbed six points clear atop the La Liga table thanks to second-half goals from Miranda and Diego Costa at Vicente Calderon.
Miranda, 29, understood the significance of a win which keeps Atletico on track for a first league title since 1996, but has already turned his attentions to Tuesday's UEFA Champions League clash against Chelsea.
"This was an important win. The team was good and we must carry on like this," the Brazilian told Canal+.
"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."
David Villa's penalty miss on 50 minutes, which saw a tame effort from the forward kept out comfortably by Manu Herrera, appeared set to prove costly for Atletico.
But Miranda's well-placed header from a Jose Sosa corner and Costa's stoppage-time penalty, which led to the sending off of Cristian Sapunaru, sealed three points for the hosts.
Miranda said the set-piece move that led to his goal was one that had been practiced several times at training.
"It's a move we've trained for, one we've worked on a lot," he said.
"We have good takers and plenty of quality players at set-pieces."
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
