Outplayed for much of the first half by the reigning champions, Simeone's side took control after the break to win the first leg 2-0 and ensure they are favourites to progress to the quarter-finals.
Simeone made seven changes to the team that beat Levante 3-1 in the league on Saturday and the Atletico boss said his squad's freshness was vital to their success at the Vicente Calderon.
“Madrid started better but my guys responded well," Simeone said after the match.
“We settled in the first half and were more competitive over time. The second half was very good. We worked well and we were tidy.
“The changes gave vitality to the team and that allowed us to occupy the spaces and close down well.
“We wanted to play our best XI and put out a competitive team, so we could have more patience and press. We pressed well in attack.
The match was fan favourite Fernando Torres' first in an Atletico shirt since his return to the club earlier this week, and Simeone insisted the much-maligned striker performed admirably despite a quiet 60-minute stint on the pitch.
“Torres showed enthusiasm, energy. He was strong and fast but needs time to get used to his teammates but as the minutes went on he felt better," he said.
The second leg of the round-of-16 tie will take place at The Santiago Bernabeu on January 15.
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