Atletico were frustrated for large parts of the fourth-round tie and had to wait until the 67th minute before breaking the first-leg deadlock.
Substitute Antoine Griezmann struck the first blow with a glancing header, before a Gabi penalty and Cristian Rodriguez's 25-yard strike made the victory more emphatic.
Simeone admitted his side had not been good enough in the first half, and praised the impact of Griezmann to lift the display after being introduced at half-time.
"We construed the match quite well," said the head coach. "In the second half, we improved our game and when Griezmann entered the match, the team grew offensively and everyone improved.
"From [Raul] Jimenez and [Alessio] Cerci to Lucas [Hernandez], who played a good match for being so young.
"In the first half, they blocked well, they had a good tactical approach to close our gaps. They made a good impression, especially for everything they did in the first half."
Atletico will host the second leg on December 18 at the Vicente Calderon, looking to reach the fifth round.
