Chelsea went 4-0 down in the first 25 minutes after an early goal by Raheem Sterling, two Sergio Aguero strikes and an effort from Ilkay Gundogan.
And it could have been worse for Sarri's side if Aguero had converted from six yards when faced with an open goal with the score at 1-0, but the Argentine fluffed his shot wide.
City went on to inflict a 6-0 defeat over the 90 minutes with second-half goals from Aguero and Sterling adding to their lead.
Speaking on Sky Sports at the interval, Carragher said: "I called a couple of Chelsea performances a disgrace going into this game, this is as bad as anything."
"Looking at Sarri, just over halfway through his first season, but the worst thing I can say is it looks like he's turned Chelsea into Arsenal. That Arsenal team that just used to get battered for the last seven or eight years away from home in big games because they were too weak.
"You could never say that about Chelsea, no matter what's gone on, that they've been 'weak,'" added Carragher. "We're watching a really weak football team here."
They are now sixth in the league table, a point behind Manchester United in fourth spot while Sunday's beating saw them drop past Arsenal on goal difference, and have suffered a slide of late with only one win in their last four top-flight games.
That run also included a disappointing 4-0 loss to Bournemouth on the south coast.
The Blues face Malmo on Thursday in Europe next time out and then host United next weekend.