The Premier League champions saw their title defence suffer a huge setback, as Pep Guardiola’s side put in a stunning second half performance to take all three points.
City’s 10th league win in a row, means they have a 10-point advantage over Jurgen Klopp’s side and a game in hand.
Liverpool have been hit with injuries this season, with Virgil van Dijk, Joe Gomez and Diogo Jota sidelined for long spells.
And Carragher admits it is hard to be “too critical” of Klopp’s side, as they lack freshness and strength in depth.
“This is a team who have gone to the well and produced unbelievable moments and trophies for this club which is why I find it a little bit hard to be too critical of this team.
“They just haven’t stopped for three years. That’s why I say they need a little bit of help.
“They need three players. A centre back, someone to replace Wijnaldum and someone to come in for the front three,” Carragher said on Sky Sports.