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The Reds crashed out of the FA Cup on Sunday afternoon, losing 1-0 to Plymouth Argyle at Home Park in the fourth round.
Liverpool had won each of their last six games across all competitions before locking horns with the Pilgrims, who sit rock bottom of the Championship.
Now, Liverpool will turn their attention to the Premier League, with a difficult match against Everton at Goodison Park on Wednesday night.
The Reds have some difficult games coming up, but Carragher seems to believe his former side have a greater chance of crowing themselves English champions now they're out of the FA Cup.
After the game at Home Park, the Sky Sports pundit responded to a tweet from an optimistic fan.
"Probability to win the league has gone up," posted @TaintlessRed on X, formerly known at Twitter.
I think we've seen during this season, we've seen a few times already, that it's a game plan, a playing style, which is difficult for our starters, but also for the ones that played today.
"So, constantly long balls, second balls, long balls, second balls.
They had a similar playing style going to a very low block [then] kick every ball long, and then we played with our starters.
"I think today also showed why we played with the ones we played with today because these players need game rhythm as well.
For them to be ready in the upcoming months, they need game time, and you saw today that some of these players really need games like this to be ready for the last three months of the season."
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