Carragher said: "There won't be any excuses if we don't do it now. We've got five home games and three away. In our position, anyone would take that for the run-in.
"If we win those home games and pick up points away from home that would probably be enough, although we'll be going out to win every match.
"It was a disappointing result to draw at Leicester and no-one will try and disguise that. But let's not forget that we're now in a better position than we were before the game.
"It may only be a slight consolation, but come the end of the season this could prove to be a very important point.
"When you look at the games we've got left, I'm sure everyone will think that apart from Arsenal, Manchester United and Newcastle, there aren't many tough matches. But it probably won't work out that way.
"We may perform better against the teams nearer the top. Ever since I've been in the first team we've seemed to rise to the occasion against the big teams."