Man City lost 1-0 to Barcelona at the Nou Camp, seeing Sergio Aguero miss a penalty, and were knocked out of the Champions League in the last-16 stage for the second year running.
And the former Liverpool man said: "Their best players are getting to that age and I think it's time for changes at Manchester City now.
"They've been fantastic but it's getting to that time and I don't think they're getting any better."
Jamie Redknapp echoed Carragher's thoughts by saying: "Last year, City competed a lot better. There was a huge gulf in class today. If it wasn't for the goalkeeper, it could've been worse. I agree with Jamie in that it's not a Band Aid situation - they need major surgery. They need three or four players to come in.
"Is Pellegrini the man to take it forward? Tactical naivety playing 4-4-2 against Barcelona. You can't do it. You'll get punished. He's lost the last 16 games against Barcelona and that isn't good enough for a manager."
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