The veteran Reds defender believes the form of other clubs could help the Anfield side rise up the table, and praised striker Luis Suarez for his current goalscoring form
The Reds made a sluggish start to the campaign under new manager Brendan Rodgers, but have shown more consistency of late with a seven-match unbeaten run, and they currently lie eight points adrift of fourth-placed West Brom.
The Baggies have been the surprise success of the season so far, but the form of other clubs with Champions League ambitions such as Tottenham, Arsenal and Newcastle has been patchy, and Carragher believes this inconsistency could open the door for the Anfield side.
"Teams are dropping points all over the place," the 34-year-old said. "We look at it as if we haven't had a great start to the season but winning yesterday we're not too far of the top four, which is where we want to be.
"From our own point of view we want to push on and make a challenge for the top four. It seems like if everyone is throwing it away it is still up for grabs."
One reason behind their success has been the outstanding form of Uruguayan striker Luis Suarez, who has scored 10 goals in 12 Premier League matches this campaign.
And after another two goals in Liverpool’s 3-0 win over Wigan at Anfield on Saturday, Carragher is full of praise for the former Ajax frontman.
"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," he told the BBC Sportsweek programme.
"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."