The Manchester City boss fired the first shot during his press conference on Tuesday when he leapt to the defence of his players amid claims of complacency following Sunday's 3-3 draw against Tottenham.
Sky Sports trio Carragher, Gary Neville and former City defender Micah Richards were targeted by the Spaniard after suggesting the Treble winners could be showing signs of complacency after last season's historic exploits.
"Gary Neville knows how difficult it is, otherwise he would have won four Premier Leagues in the best period of Manchester United," said the Man City boss. "But he didn't do it. Maybe they accuse us of complacency because they felt complacency (at United). Maybe they felt it. This team so far, no chance.
"Jamie Carragher didn't win one (title). Micah Richards didn't win four Premier Leagues in a row. Never, ever. It's never happened.
"I don't have anything to say about the pundits, honestly. It's not about that (complacency). Maybe I'm wrong but I don't think it's about complacency."
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Carragher immediately fired back at Guardiola claiming he would have won a title had Liverpool been under state ownership during his playing days.
The ex-Reds defender posted on X: "I think I'd have probably won one if Liverpool were owned by a nation state, and pushed the rules so far that the PL charged us 115 times!
"I was actually praising Pep's team after the game on Sunday," he wrote alongside a laughing emoji.
City currently sit in third place on the table, six-points adrift of leaders Arsenal ahead of Wednesday night's trip to Aston Villa.
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Guardiola's side are on a run of three-straight Premier League draws after previously struggling to find a way past Chelsea and Liverpool.
But with Arsenal showing signs of momentum and Liverpool staying on the heels of Mikel Arteta's men, City have no room for error and upcoming involvement in the FIFA Club World Cup could see the Treble winners slip further behind the chasing pack.