The Red Devils won their opening game 1-0 against Wolves but fell to a 2-0 defeat against Tottenham at the weekend.
A trio of Casemiro, Bruno Fernandes and Mason Mount have all been named in the middle of the pitch for United so far.
However, Wolves and Spurs have both found it easy to navigate their way through the midfield, especially the latter on Saturday night.
It's something that Carragher has identified as a big problem for Erik ten Hag's side after just two games of the season.
"The set-up of the midfield is not right for me," he said to Sky Sports on Monday Night Football when analysing clips of United against Spurs.
READ MORE ON MANCHESTER UNITED
Mason Greenwood offered escape route out of England following Man United statement
Mason Greenwood vows to become 'better person' as he releases statement
"I'm going to look at Casemiro but I think there's a few things wrong, I think the manager's set-up, what he's asking them to do, and the set-up in terms of the profile of players is not right."
When talking about the midfield players' positioning, he added: "The reason why I don't like the set-up of the manager is because he plays a man-marking system. You see how disconnected the United midfield three are because they go man-to-man.
"This guy in midfield [Casemiro], as we saw on Monday night and we saw constantly on Saturday night, is being left exposed in the middle of the pitch on his own, and he can't cope.
"In this situation, James Maddison just runs on the back of him, gets away from him and again, you're right at the United back four."
Most read in Football
Guardiola surgery as City agree £55m deal, West Ham to sign defender, Roma eye Greenwood
Mason Greenwood offered £10m-a-year move abroad to link up with Liverpool legends
Pep Guardiola undergoes emergency surgery and will miss Man City's next two PL games
Tottenham 'blackmailed' Bayern Munich into signing Harry Kane for £100m, insists club icon
In another clip, he had more of a focus on Casemiro: "He plays a nice pass in but this is about nothing else but Casemiro. He makes a decision to go, when this ball is turned over he should hold his position, he goes flying in there, so does Mount.
"But, he's bypassed so easily by Maddison when he get's there. Maddison is a good player, technically good but he's not quick and that is far too easy and again, right through the heart of the United midfield."
"We talk about him being left exposed," Carragher went on to also say. "But when I stop this clip and here and you look at how many men United have in probably a 20 by 20 [area].
"Casemiro at the back there, it's a six v four, he [Destiny Udogie] turns and he just runs at Casemiro, I mean that is not acceptable, it's not at any level, certainly a player of his quality and experience over the years."
Carragher then said he would be worried about Casemiro's start to the season as well as United overall makeup in the midfield.
He also pointed out that the Brazilian has been dribbled past six times this season when playing in his role, double that of Chelsea and Liverpool's respective stars Conor Gallagher and Alexis Mac Allister.
Casemiro was a key figure for United last season but already appears to be struggling in system so far this term.