The Uruguay international produced another scintillating performance in the 3-0 win over Wigan, scoring twice and having a hand in another goal as the Reds recorded only their fourth home win of 2012.
Brendan Rodgers' side are now only four points behind perennial Champions League qualifiers Arsenal, in sixth, and eight behind surprise package West Brom, currently occupying fourth place. Carragher said: "Teams are dropping points all over the place. From our own point of view we want to push on and make a challenge for the top four."
He added: "It seems like if everyone is throwing it away it is still up for grabs."
Carragher came off the bench late on, which gave him chance to appreciate fully Suarez's performance. His first-time strike from Raheem Sterling's cross was matched only by his cool finish when played through by Jose Enrique, who then clinched the result with his first goal for the club after he followed in the rebound from Sterling's shot.
Carragher rates Suarez as high, if not higher, than the great forwards he has played alongside at Anfield and feels he is irreplaceable.
"I think he is definitely right up there," he told BBC Radio 5 Liver's Sportsweek. "I can only talk about the players I've played with (Robbie) Fowler, (Michael) Owen, (Fernando) Torres and I think he comes pretty close to that list.
"It's not a great Liverpool side at the moment. The other players I've played with have played in sides that have won trophies and been near the top of the league.
"For him to do what he is doing in a side that is still building under the new manager I wouldn't swap him for anyone in the Premier League.
"I think what he does in our team and what he gives us no other player really could."