The former Liverpool hero says the defender has let himself and the club down badly after being called up for allegedly failing a drug test.
Sakho is claimed to have been found with a banned fat-burning substance in his bloodstream after the Europa League win over Manchester United last month, and has been made temporarily unavailable for selection by the Reds.
Though he has not officially been banned by UEFA as of yet, if an investigation finds that the claims are substantiated, he would be likely to face a ban of over six months, ruling him out of Euro 2016 and the opening months of the next domestic season.
Carragher, who played over 700 times for Liverpool throughout his career, believes there are now "serious questions" to be asked of the French centre-back and insisted that the alleged violation is unacceptable.
The defender-turned-pundit told Sky Sports: "It's a nightmare for the player. I think he's let himself and the club down badly, because he's become a really important player. There's serious questions to be asked of him.
"He's had a great campaign. He's one of the leaders of the team now, certainly within that run, thinking about how well he played in the Manchester United and Borussia Dortmund games. It's now how Liverpool fill that void. For a professional footballer, as in any sport, it's not acceptable.
"How much is enough [to be tested], or too much? As a player it would happen two or three times a season. People might say that's not enough. But there seems to be a lot more of that goes on in other sports, not something you'd expect from football."
As alluded to by Carragher, Sakho's absence will come as a big blow to Jurgen Klopp and the Liverpool side as the 26-year-old's recent displays have been much improved from the inconsistent, error-strewn performances of his early Anfield career.
He has now established himself as a first choice in the centre of defence, and Klopp must now consider other options both for the remainder of the current campaign and, potentially, in the long run.