Kompany was taken to hospital after collapsing while watching the club’s second team practice.
He was suffering from a virus and missed the pre-match press conference on Tuesday for Bayern’s Champions League match against Arsenal.
Kompany was on the sideline for Wednesday’s match and Eberl wondered if he “should have reined him in earlier.”
“The fact is we protect our coach wherever we can,” he said.
“If a coach says he feels ready to do something, then we’re not going to say ‘we won’t allow that’ if we don’t know what’s going on.
“It’s also everyone’s responsibility to say, ‘I can’t continue now.
“Vinnie is a hard worker. If you don’t listen to the subtle signals your body is sending, it will eventually scream in pain.
“Vinnie will have this time (now) and we will continue to try, even more than before, to protect him from himself.”
Kompany spent 11 years at Manchester City as a player, winning four Premier League titles, two FA Cups and four League Cups, before becoming a manager with Burnley.
After guiding them to the 2022-23 league title, Kompany has failed to keep the Clarets in the Premier League.
He left to take charge of Bayern in May 2024 and led them to successive Bundesliga titles.
Kompany’s assistant Aaron Danks spoke to the Bayern boss in hospital.
“I explained to him that we wouldn’t have conversations about football,” Danks said. “It was just a matter of checking on him and making sure he was OK.
“All football operations are in our hands and we will work together as a team to move the club forward.”
Gn sports
