Carragher had been backing Liverpool to beat United to a top four spot, but their current league position has caused him to change his mind.
He said when asked if he still believes Liverpool will finish higher than Louis van Gaal's side: "Not now no, I have to go back on that one."
United have a six point gap over Liverpool with seven games left remaining. It is not inconceivable the Red Devils let it slip, but they are currently in good form.
The Red Devils won 2-1 at Anfield at the end of last month, and Brendan Rodgers' side followed that up with a 4-1 loss away at Liverpool.
United do not have a top four place sewn up yet though. They may have beaten Liverpool, but over their last seven games have tough fixtures against Manchester City, Chelsea and Arsenal all to come.
If they lose two of those and Liverpool can get back on form there is still a chance of a turn around, but Carragher's belief United will see out their advantage is the most realistic outcome.