Asked whether Rafa Benitez was the right man to end an 18-year wait for a 19th League title, Carragher replied: "Only time will tell and I haven't a clue.
"Rafa has done very well but the League is the one we want and it doesn't look like it's going to happen this season.
"We'd need an unbelievable second half to the season, while those above us would need an unbelievably bad one. We realise the cups represent our best chance of silverware this season - that's why they're so important.
"We haven't won the League for such a long time and it'd be lovely if we could do it before I finish. You could say the spending power of other clubs is making it more difficult. But then you look at Arsenal and what they've done under Arsene Wenger without spending big and you realise you just have to get on with it."
Carragher, 30 in 10 days, marked his 500th appearance by wearing the captain's armband as Liverpool provided some respite for Benitez by sweeping aside Luton in Tuesday night's FA Cup third-round replay.
He added: "You can't hide behind excuses. Results haven't been good enough because we haven't been good enough. End of story.
"It's not just a question of whether the manager is good enough. The same applies to the players and we all know we have to improve."