O'Neill parted company with the 16th-placed Black Cats this weekend - and journalists asked Rodgers for this thoughts following our 2-1 win over Aston Villa on Sunday.
"Whenever someone of the status of Martin O'Neill loses his job then we've all got to be on the back foot," said Rodgers.
"This is a guy with many years of experience and went into Sunderland and picked them up off their knees. It's obviously a difficult time but he's still a top-class manager.
"I hear the same things about Stoke and Tony Pulis. I think they need to be careful, some clubs. They need to understand where they're at and that they won't always be on the front foot going forward.
"If you ask clubs like Leeds and Portsmouth and Barnsley, teams that were in the Premier League, I think they'd be happy with Tony Pulis, Martin O'Neill and guys like these.
"Guys like Martin O'Neill losing their job - it's a sad day."