The Red Devils could not hold on to the three points in their dramatic 3-3 draw against Everton.
In reaction to the result at Old Trafford, Solskajer said on Saturday: “We're not talking about winning titles.
“We shouldn't even be considered as title-chasers. That's one for you [the media].”
And this comment left Carragher stunned, believing United had given up hope on the title.
Speaking on Sky Sports ahead of the Anfield clash, the pundit said: “I think it's only Liverpool who can stop them - I don't think Man Utd fancy it.
“Listening to the comments of the Manchester United manager, they just seem happy to be involved - I cannot believe it.
“It's a unique season; Liverpool have no centre-backs, City have had no strikers and De Bruyne has been out.
“We were saying last season that City were off the boil - they're only three points better off so it shows they're still not the City of two, three years ago
“I think Man Utd have bottled it now they've got there, they've almost talked themselves out of it with their last results.”
The Chelsea legend told talkSPORT last week: “I’ve said Man City from the start.
“We played against them recently, and they are the kind of team that, no matter how you play, if they are on it, they can beat anyone in the league.
“When you play against them the movement is incredible and you really don’t know what to do.
“It’s one of those games where you come off and can only learn from it really, how well they move and the options they give each other on the pitch. They make it so difficult for the opposition team.
“So they are the ones for me.”