Diego Costa's 11th-minute strike was enough to secure the win at the Santiago Bernabeu, and the Argentinean boss was quick to praise his players after the game.
"They played extraordinarily well," Simeone told reporters. "From their intensity to knowing where to cause harm [to Madrid]. I congratulate them because they have responded really well in an important game. We only speak about ourselves, [and] I believe we interpreted the game well.
"We understood that we could take advantage of Diego Costa between the lines and David Villa played the perfect game tactically. We missed a couple of great chances in the one-on-one.
"But the players stood up: from the first to the 18th [of those called up], we knew there was only one option: and that was to win the game. The loyalty to the team and the club depends on all of us."
The result keeps Atleti joint-top of La Liga alongside Barcelona.