Following a 5-0 defeat at Manchester City, Jurgen Klopp’s side having now won just one of their last eight games in all competitions.
Manchester United held them to a 0-0 draw in their latest outing, and the former Anfield icon believes the club must now shift their focus.
Carragher told Sky Sports: "Liverpool will be looking around the clubs going for top four and how far they are behind those positions.
"Even at the start of the season I don't think Liverpool fans expected them to win the title - I certainly didn't.
"Liverpool will be more interested in Arsenal's results - maybe Chelsea and Tottenham - although those two probably think they're capable of catching the two Manchester clubs."
Stalemate against United has left Liverpool eighth in the Premier League table, nine points adrift of leaders City and two behind Watford in fourth.
Carragher believes that Klopp missed a trick against the Red Devils, forsaking the possibility to score a morale-boosting victory had they shown more ambition.
He added: "Jurgen Klopp made changes but he still kept the three-man midfield the same.
"Manchester United showed such a lack of ambition it was worth taking a risk by leaving Coutinho on and bringing on another attacking player.
“Yes, you can get done on the counter but it was obvious United were here for a 0-0 and hoping to nick a goal from a set-piece or a counter-attack.
"I think Liverpool should have taken the risk to take [Georginio] Wijnaldum or [Emre] Can off.
"It's not easy as a manager but I'd have taken that chance earlier and the substitutions shouldn't have been just player for player, but more tactical.
"It would have given Liverpool an extra attacking player on the pitch - it could have cost them the game.
"But it could have won them the game - but the position Liverpool are in, it was a game they had to go for."
Liverpool are back in action on Tuesday (19:45) against Maribor in the Champions League.
