Liverpool are preparing for a crucial clash with Galatasaray in the Champions League on Wednesday as they aim to bounce back from a 1-0 loss in the first leg last week.
Confidence is low in the squad following the 1-1 draw with Tottenham at the weekend which saw supporters leave early and boss the side after the final whistle.
Speaking ahead of the Galatasaray clash, Carragher believes Slot has a long way to go before supporters are back on his side.
"It's worrying, in terms of what Liverpool do this season," Carragher noted. "The bigger point is how worrying it is for the manager. I think there's a difference with most support in terms of what we see online compared to the match-going fans.
“It's not easy for a Liverpool crowd to turn on a manager who has won a title less than a year before, but I felt there was a big shift on Sunday in terms of how the crowd felt about the team and the manager.
“The booing at the end, that was proper booing from a disgruntled and unhappy fan base. I think it's going to be really difficult now for Arne Slot to get them back. Once you lose that crowd, it's really difficult to get them back."
The Reds have won only 46.7 percent of their Premier League games this season and their European hopes hang by a thread heading into Wednesday’s clash.
If Liverpool are knocked out, there only chance at silverware would be the FA Cup where they next face Manchester City.