The former Liverpool defender, speaking in his role as a Sky Sports pundit after the match, believes there are two players Jurgen Klopp must replace this summer.
Carragher is adamant that neither left-back Alberto Moreno nor goalkeeper Simon Mignolet should be part of Liverpool’s long-term future under Klopp - scroll down this page to read his comments - and one suspects plenty of fans will agree.
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“The left-back [Moreno] has to come out of the team,” Carragher was quoted as saying after the match by the Liverpool Echo. “This is not a one-off today in terms of the goal.
“[Jon] Flanagan has come back fit and has to go into the team in midweek, he [Klopp] has to change the left-back.
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“Flanagan played left-back when they nearly won the league. He can't be worse than him [Moreno].”
Carragher explains why Mignolet must also go
Mignolet was at fault for Fernandinho’s opening goal but redeemed himself with a string of top saves.
However, Carragher feels that Liverpool are in desperate need of a more reliable keeper from the start of the 2016-17 campaign onwards.
“The goalkeeper has made some outstanding saves today, but just because you make some outstanding saves doesn't mean you should be allowed to concede a goal like that,” Carragher continued. “And that is not just today.
“Going forward for Liverpool, those are two areas Jurgen Klopp has to change in the summer.
“The goalkeeper may have signed a five-year deal, and he has made some good saves today, but things have to change.”
Carragher's analysis of Man City goal
Analysing Manchester City’s goal, Carragher added: “It starts with the left-back Moreno. He splits initially from a goal kick, but now he knows isn't going to receive the ball he has to get back.
“Sergio Aguero is in the right position to pick up the ball because his opposite full-back has gone in to go for a header. And then he (Moreno) doesn't see the run.
“But that (the goalkeeper) is shocking. You can't score from there.”
Moreno: More a left-winger and less a left-back?
Carragher has been critical of Moreno on several occasions this season. The 23-year-old is terrific going forwards but lacks defensive intelligence, suggesting he might be more suited to the left-wing position rather than left-back.
Liverpool face competition if they want Ter Stegen
Mignolet, meanwhile, has made a string of costly errors this season and many fans were gobsmacked when the Belgium international signed a new five-and-a-half-year deal last month.
The Reds have been linked with a move for Barcelona’s Marc-Andre ter Stegen, who only plays for the Catalan giants in cup competitions, but they now face competition for the Germany international’s signature from Manchester City according to the Mirror.
Liverpool fans: do you agree with Jamie Carragher that Jurgen Klopp must replace Simon Mignolet and Alberto Moreno? Let us know by leaving a comment in the box below.