David Villa put the capital side ahead after a 15 minutes before Diego Costa's penalty doubled the advantage for the hosts.
Rodri halved the deficit before half time but Atleti demonstrated their clear superiority in the second period, which saw Tiago and Raul Garcia both score to pave the way for a comfortable victory, with Alex Vidal's late strike a mere consolation for the Andalusians.
Simeone, speaking to journalists after the game, stressed that he was pleased with the manner of the win and his team's instincts with regards to closing out the match.
"These games are very dangerous," the 43-year-old Argentine said.
"The rival was in theory a much lower standard, so I'm very pleased with how the team faced the game, the players knew how to interpret it.
"We were able to kill it off when we needed to.
"They were not an easy opponent. We found a team that comes to score in every game. We knew we have good individuals, and in the important parts of the game, we were strong."
Atleti have now won four in a row in La Liga this season, scoring 14 times in the process, and Simeone was keen to single out the contribution of Portuguese midfielder Tiago in particular.
"I always say what I think of him [Tiago]," he added.
"He's very important player for the team. But that is what so great about this squad- all players know that one day they can play and another to be in the stands but all are essential."
Simeone's team host Zenit St Petersburg on Wednesday in their first Champions League group game of the season.