Chris Sutton believes Wilfried Nancy's Celtic departure was "inevitable" following their defeat to Rangers, but insists the problems at the club run much deeper.
Nancy has been dismissed after losing six of his eight games in charge, with Saturday's Old Firm collapse the final straw, and the club have on an interim basis.
The Frenchman, who signed a two-and-a-half year deal, lasted just 33 days after the club's form slumped dramatically after they had won seven of their eight games under O'Neill.
Rangers are now level with Celtic in the Scottish Premiership, with leaders Hearts six points ahead, but Sutton believes the decision to part ways with Nancy has boosted their chances of winning a fifth straight title.
"Keeping Nancy in position would have been too much of a risk. He was a stickler, set in his ways," the former Hoops striker told Your Site News.
"It's a bit like the Ruben Amorim situation at Manchester United but over a shorter period.
"He was fixated on changing Celtic's style, moving to a 3-4-3, playing one particular way. He just wasn't adaptable and for Celtic to lose six and ship as many goals as they did - it was kamikaze stuff from Nancy.
"The game before Rangers, the Motherwell loss, the manner of the loss was humiliating.
"A lot of Celtic fans thought at that moment it was time for Nancy to go. He took charge of the Rangers game and Celtic played well, but a theme of performances has been to play well in patches. They showed too much vulnerability.
"There was an inevitability that Nancy would head out the door. It's the right decision; Celtic have to give themselves the best chance of winning the title."
Head of Football Operations Paul Tisdale, who played a huge part in bringing Nancy to Celtic from Columbus Crew, has also left the club.
"Nobody knows what Paul Tisdale was doing at the club. Dr Do-little," the former Celtic striker added.
"He had a large say in bringing Nancy in, and if he had a hand in recruitment over the summer that was also poor. It's the right decision for him to part ways.
"Now Celtic are under pressure because this squad needs strengthening in January and quickly.
"The players have to take their share of responsibility. Poor form has not just been under Nancy; there were issues at the start of the season.
"Brendan Rodgers wanted more quality brought to the club, that didn't happen. It was an unsavoury end."
"Things brightened up a bit under Martin O'Neill, he did a brilliant job, but the team weren't playing particularly well.
"Nancy came in and tore everything up, but the problems do run much deeper than Nancy."
Nancy's coaches Kwame Ampadu, Jules Gueguen and Maxime Chalier have also left, with O'Neill in charge for Saturday's league game against Dundee United alongside Shaun Maloney and Mark Fotheringham.
Speaking before O'Neill was reappointed, Sutton said: "Short term, the safest move would be to bring Martin O'Neill and Shaun Maloney back.
"It's just about winning games now. Martin did brilliantly in a short space of time.
"Knowing Martin like I do, he knows the club need to add in January. That's the most sensible option."
O'Neill, 73, returned to the Celtic dugout in October, 20 years on from his first spell as Parkhead boss, after Brendan Rodgers' resignation.
They won all four of their Premiership games under the Northern Irishman and also beat Rangers to reach the League Cup final, which Nancy's side lost to St Mirren.
