Jamie Carragher said Manchester City are facing a battle to finish in the top four after their 2-0 loss to Liverpool on Sunday left them 11 points behind the Premier League leaders in fifth.
City's fourth consecutive Premier League defeat stretched their winless run to seven games in all competitions as a first-half goal from Cody Gakpo and a second-half penalty from Mohamed Salah secured a dominant victory for Arne Slot's side.
Pep Guardiola held up six fingers to the home fans, in reference to his Premier League title wins, as they taunted him with chants of, 'You're getting sacked in the morning', but Carragher feels City are now out of the race this term and warned they should start looking over their shoulders.
"I don't see there's any way back for Manchester City now," Carragher said on Sky Sports.
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"Sometimes you need to lose so people realise what you've done so you don't take it for granted. And maybe he's sending a message to the hierarchy, the people above him and the fans.
"But this season Manchester City will not win the Premier League."
Carragher highlighted their issues in midfield, where Rodri is sidelined for the season with a knee injury, and likened their plight to Liverpool's during Jurgen Klopp's latter years in charge.
He added: "It's a mini-crisis for Manchester City. I think it's reminiscent of Liverpool two years ago.
"I actually think they might have a fight on their hands for the top four.
"I look at Arsenal, Chelsea and the way they are looking right now and I think it will be difficult for Man City to finish above them if they don't go into the market in January.
"I go back a couple of years to the season Man City won the treble. Liverpool went to the Etihad in April and got beat 4-1. It could have been six or seven. They got absolutely battered and you felt like it was the end of that Jurgen Klopp team.
"But what it was was the end of that midfield, of Jordan Henderson and Fabinho. No matter how good a manager you are, you can't fix that.
"I don't think Pep can fix City's midfield now. He needs to buy players there. If he can do it in January, who knows, but he may need to wait to the end of the season.
"Right now, I can see Man City losing another four or five games between now and the end of the season. I look at the energy of Chelsea and Arsenal and I think it will be difficult for City to finish above them."
The defeat, during which City were overrun in the centre of the pitch, sees them drop below Arsenal and Chelsea, who beat West Ham and Aston Villa respectively this weekend, and also fourth-placed Brighton.
"Man City at one stage in the second half had Rico Lewis and Bernardo Silva in central midfield," continued Carragher. "I love Bernardo Silva. What a player. But he's not a central midfielder. Rico Lewis is a decent player but it's nowhere near enough.
"Look at what Arsenal and Chelsea have got in central midfield, the energy, the power. They can't compete with that at the moment, Man City."
Keane: Never felt like Liverpool would lose
Roy Keane praised Liverpool's display and highlighted the importance of their winning mentality under Slot. The win means they are nine points clear of second-placed Arsenal.
"We have to praise the manager Arne Slot as he's doing a magnificent job but the squad he took over were a decent group," said Keane.
"He's added his personality to it. If you'd have been told that Liverpool would be in the position they are now, you wouldn't believe them.
"Their performances, their defence, their big players are turning up for the big occasion. They were awful against Southampton but still scored three goals and won the game.
"It never felt like Liverpool were losing today. It's a combination of decision-making and quality.
"Man City didn't show that intensity. Walker switches off for the first goal. At the moment all their players are just off it and so it's like the perfect storm for their opposition."
Carragher felt Walker's role in Gakpo's opener was reflective of his decline into a "liability" for the champions.
"He can switch off and that's always been the negative about him," he said. "He doesn't look again and switches off.
"That has been a problem throughout his career. That is nothing to do with his age.
"He has become a little bit of a liability for Man City."