A goalless draw in a relatively uneventful 220th Merseyside derby meant they could not close the gap on Everton, five points ahead in sixth place.
With two matches remaining it seems likely Brendan Rodgers' side will have to settle for seventh as nearest challenges West Brom are seven points behind with a game in hand.
That is one place better than 12 months ago, having already surpassed that points total, and they are currently 12 points adrift of Champions League qualification as opposed to the 17 in Kenny Dalglish's final campaign in charge.
But Carragher, in echoing the sentiments of captain Steven Gerrard on the eve of the derby, said finishing above Everton - their only remaining target - was not a significant factor at the end of the season.
"We've got two games to go and we can't be thinking about how Everton get on," said the 35-year-old centre-back, who will retire later this month.
"If we can finish above them then great but, as Stevie said before the game, we shouldn't be getting too concerned about whether we finish sixth or seventh.
"If it is was the difference between finishing in the top four or not then of course it would be massive.
"But whether we're sixth or seventh, it's not the end of the world."