The defeat made it seven games without a win in all competitions since the turn of the year, and Atletico slipped down to seventh in the standings, five points short of the Champions League qualification places.
"We have hit rock bottom in terms of play and results, we can't do any worse," Aguirre said after the game.
The former Mexico boss said president Enrique Cerezo came down to the dressing room to speak to the players after the match at the Calderon, where fans barracked the side once again as they left the pitch.
"Cerezo had strong words with the players and myself, but I am not going to reveal what he said. That stays in the dressing room. He wasn't pleased and showed his feelings," Aguirre added.
"I have a contract until the end of June which I signed in front of two people. Neither of them have said I am not going to continue in the post. I will continue to do my best and I hope that at the end of the season we can finish in the top four."
Cerezo sought to play down his meeting with the players and Aguirre, in quotes carried on the Marca website.
"They are the ones who have to turn it round. All I can do is try and encourage them," Atletico's president said. "I am not considering the sack."
Atletico have just over three weeks to find some form before the Champions League first knockout round gets underway. They host Porto in the first leg on February 24.
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