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Haaland was a substitute in Manchester City's 3-1 defeat at the Bernabeu, having been deemed unfit to start, and is a doubt for Sunday's Premier League clash against Liverpool.
Working alongside Micah Richards and Thierry Henry in Spain for CBS on the night of the game, Carragher suggested the 24-year-old didn't fancy a duel with Real centre-back Antonio Rudiger.
"So let me work this out.
Haaland has gone to the manager this morning and said he's not fit?" the Liverpool icon questioned.
"Do you think it's got something to do with Rudiger?
I never went to see the manager on the morning of a game and said I'm not fit.
So he's injured, is he?"
Carragher then left Richards particularly disappointed by adding: "It's Rudiger-itis, is it?
I don't know why he makes that suspicious, you know that?
"Did he say that Haaland didn't want to play the game?
It's not nice — and it's not true.
"He was crazy to play the game but had a problem with his knee and could not play."
Carragher wasn't happy that the tone of questioning painted his comments as if they were serious and leapt onto social media to clarify.
"It was a joke to wind up Micah Richards as that's the nature of our show on CBS," the 47-year-old posted on X in an attempt to defend himself.
Haaland is suffering from a knee injury and faces a late fitness test to determine whether he can feature against Liverpool.
Arne Slot's league leaders visit the Etihad Stadium aiming to extend their advantage over Arsenal to 11 points with 33 left on offer.
The Gunners' faint title hopes were dealt a hammer blow on Saturday as Jarrod Bowen's goal earned West Ham United a 1-0 win at the Emirates Stadium.
Carragher's comments will undoubtedly serve as motivation for Guardiola and Haaland to play their part in offering Mikel Arteta a reprieve against Liverpool.
For more news relating to West Ham, visit our sister site WHU Latest Live.