With both sides gunning for the Premier League title, there was a big build up to the aforementioned fixture.
The Reds struggled to get going in the first-half. The Citizens took a 2-1 lead into half-time as a result.
However, Jurgen Klopp's team responded after the break and ended up securing a 2-2 draw against Pep Guardiola's side.
Carragher believes that a shift in mentality allowed Liverpool to walk away from the Etihad Stadium with a point.
As quoted by Anfield Watch's Twitter account, the Scouser told Sky Sports the following: "The performance from Liverpool not so much in terms of quality but their mentality to come out in the second-half. They'd been given the run around in the first-half.
"I don't think they did anything completely different. They didn't change. These teams believe in what they do and rightly so. To come out in the second-half and match City, maybe do better, I was so impressed with both sides today."
Anfield Watch Verdict
We completely agree with Carragher's take. Liverpool looked more confident in the second-half against Manchester City, which can be put down to a shift in mentality.
Klopp's side simply looked nervous in the early stages of the clash, and the Citizens took full of advantage of that.
"I think there were a few nerves in there at the start - it was understandable - one of the biggest games in Premier League history," the 23-year-old told beIN Sports, as quoted by Anfield Watch on Twitter.
"You know how many people were watching, but after that, we settled down."
In terms of the Premier League table, nothing has changed after yesterday's match. League leaders Manchester City still possess a one-point lead over Liverpool.
Both teams have seven top-flight fixtures remaining.