The Liverpool boss has lamented the instability of Premier League management after the 61-year-old was dismissed by Sunderland following defeat to Manchester United
The Northern Irishman was sacked by the Black Cats following their 1-0 defeat to Manchester United at the Stadium of Light on Saturday.
However, Rodgers insisted the Wearside club may not be rewarded for their decision to part with his fellow Northern Irishman and lamented the managerial instability at many clubs.
He told the Reds’ official website: "Guys like Martin O'Neill losing their job - it's a sad day. Whenever someone of the status of O'Neill loses his job then we've all got to be on the back foot."
"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."
The Reds defeated O’Neill’s former club Aston Villa 2-1 on Saturday, and Rodgers also backed Villa’s current manager Paul Lambert in his side’s battle against relegation.
"Paul Lambert is a top, top manager. You saw what he did with Norwich," added Rodgers.
"The problem as a manager is you don't have a debut as a team. Individuals have debuts but as a manager you have to try and work with what you've got, improve it and make it better.
"The longer he is there, the better Aston Villa will become. There is no question about that. You see the fight and the energy the players here have got. Once he's brought in the profile of players he wants, they'll keep moving forward."
Rodgers refused, however, to compare his own appointment at Anfield to that of Lambert's at Villa, despite the pair arriving in the Premier League at the time same with Swansea and Norwich respectively.
He commented: "No, it's not the same. It's incomparable. Managing Liverpool is a huge honour, a real privilege.
“To manage a club with five European Cups and 18 league titles, and expectancy every single day of your life, it's incomparable to most clubs."