Defeat at West Ham on Wednesday night left them 17 points off the pace in seventh, still without a win in the league since Boxing Day.
Boss Rafael Benitez is confident they can earn a top-four place but Carragher is ready for a fight to get back into Europe's elite for the next campaign.
Carragher conceded the injury-time penalty at Upton Park, although it was problems elsewhere that led to Liverpool failing to earn their first league win of 2008.
"I don't think it's down to luck or anything like that - I've always said you get what you deserve in football and if results aren't going well like they're not at the moment that's something we've got to turn around quickly," Carragher said.
"The teams at the top are a long way away and we've got to just focus on the Sunderland game on Saturday and try and get three points from that.
"It's been a few games now since we got all three points and we need to get more points on the board."