The Liverpool has said he is 'sick' of hearing excuses for United's lack of success under Solskjaer despite their big spending and strong squad.
The Red Devils enjoyed a very productive transfer window, acquiring England star Jadon Sancho, World Cup winning defender Raphael Varane and they also re-signed five-time Ballon d'Or winner Cristiano Ronaldo.
However, the season hasn't started the way Solskjaer would've liked, with Man United already out of the Carabao Cup and in danger of not making it out of a relatively easy Champions League group.
There have been calls for Solskjaer, who's been in charge since December 2018, to go but the likes of Neville and Keane continue to back him.
And this really grinds the gears of Carragher, who suggested Neville and Keane are always looking for something else to blame when trying to find a reason for Man United's lack of recent silverware.
Speaking no the aptly-titled Tony Bellew is Angry podcast, Carragher said: "Recently what's got me angry? It's probably something to do with football and probably something to do with Neville, let me just think…
"He's permanently making excuses for his mate Ole, isn't he?
"I do a newspaper column and I was with Gary Neville a few days before, we were doing this YouTube chat about the season with Roy Keane, and the two of them were making excuses for Ole because he's played with them and he's their mate.
"They're sort of saying 'they can't win the league, they still lack this, they still need that, the Glazers aren't putting enough in, they should be going for Harry Kane…'
"I'm sitting there thinking, 'you've just signed a fella that's won the Champions League four times [Ronaldo]!
"You've spent £75million on a winger [Sancho], you've finished second in the Premier League last season, you didn't lose a game away from home [in the league]… there's only one place to go!
"Honestly… it just wound me up and I thought, 'that is it, I'm doing my newspaper column on it.'
"Ole wasn't too happy with the column, but I just said it's time the excuses stop at Manchester United, I'm sick of it.
"It's always, 'they still lack this, they lack that' - every player's on £50million!
"You go through the whole team, it's unbelievable!"