Liverpool put their recent home woes behind them to record the priceless victory, with Diogo Jota returning to his old stomping ground to score the only goal of the game on the cusp of half time.
The victory has taken Liverpool up to sixth on the league table but the defending champions are still five points behind Chelsea, who occupy the final Champions League spot.
Carragher told Sky Sports: “It's been a freak [season] and the other teams [they've lost too].
“At this moment, I still believe Liverpool will miss out on the top four.
“However, they need to make teams like Leicester and Chelsea nervous and see what they can do.
“With four or five games to go, they need to be in a position where they can jump on any mistakes the teams above them make.”
Liverpool are next in action after the international break when they travel to Arsenal on April 4.
Should Jurgen Klopp’s men miss out on a top four place, they can still play in the Champions League next season if they win this season’s competition.
