The former England defender says Pogba, 23, has flattered to deceive in his first full season in the Premier League after being signed for a world-record £89m ($109m) transfer fee from Juventus last summer.
The France international has made 25 league appearances for United this campaign, scoring just four goals.
Carragher feels Pogba has not improved the defensive side of his game over the course of the season despite being frequently used as a deep-lying midfielder by United boss Jose Mourinho.
"He's still nowhere near good enough or disciplined enough to play in that central midfield role," he told Sky Sports.
"He's a liability defensively, there's no doubt about that. They should have lost the EFL Cup final [against Southampton]. Against one of the top sides I think they would have lost that game and Pogba was one of the reasons why."
Pogba came in for further criticism over the weekend for his sloppy performance in United's 1-1 draw with Bournemouth at Old Trafford.
Carragher added: "When you have a £90m price-tag on your shoulders, we analyse more and we want more. I'm still wondering, what's his best position? What kind of player is he? What does he want to be?
"I feel a little bit like he has fallen in between everything. When you pay £90m you want to see results, and he hasn't quite delivered. He's young and he possibly will do, but as it stands he hasn't been a game-changer.
"We need to give him time. We need to flip forward to next season and see if he's improving his game. But at some stage he has to be that dominant midfield player because I do believe that's in him."
United are sixth in the Premier League, three points behind fourth-placed Liverpool. They next face Russian club Rostov in the Europa League round of 16 first leg on 9 March.