Aguirre worried about Aguero fitness
The Primera Liga side's most gifted player, 20, has been struggling with a lingering groin injury and has not looked sharp.
"This injury causes persistent pain. It doesn't stop you playing but if you overdo it, it eats away at your fitness and morale," Aguirre said in an interview with Spanish sports daily Marca on Tuesday.
"He is young and has just started dealing with it, but he doesn't have much experience. I want to protect him."
Aguirre added he had no intention of quitting despite home fans calling for his sacking after three consecutive defeats last week that have lead Atletico to slip out of the top four and left them with a mountain to climb in the King's Cup.
Defeats away to Valencia and at home to Athletic Bilbao have dropped Atletico down to fifth in the league, and on Wednesday they travel to face Barcelona seeking to overturn a 3-1 deficit in the second leg of their Cup last-16 tie.
"It isn't easy because I feel helpless (when fans in the stadium chant for you to go)," said Mexican Aguirre.
"In a one-on-one in the street I could explain why I am not going to go, that there is a project, commitment and still a lot of enthusiasm in the Cup, the league and the Champions League.
"I still have much to do with Atletico."
Club president Enrique Cerezo called for patience from fans after Sunday's 3-2 defeat against Bilbao at the Calderon.