The club may have lost just one game in the top flight so far, but they have the fourth-worst defence in the division, having conceded 11 goals and kept just two clean sheets.
Liverpool have been roundly praised for their flair up front, but the club are struggling at the back, and that is why Carragher believes that the fans are not enjoying what they see.
During Sky Sports' Monday Night Football, the player-turned TV pundit spoke of the nervousness that the team created during Saturday's 3-2 victory over Leicester City.
"I think watching Liverpool now is the hottest ticket in town," said the 39-year-old. "I think if Liverpool are on TV everyone wants to watch, but I think if there's one set of supporters who aren't being entertained by it, it's Liverpool supporters.
"Entertainment for me means you enjoy it. Now I was watching Liverpool in the pub, the game was on, it goes 2-0, it goes 3-1, no one can relax. Everyone is still on edge because Liverpool at the moment should be killing teams off.
"But what Liverpool do is give them oxygen, teams think they've got a chance against them because history has shown over the past couple of years they always concede goals."
The Merseyside outfit have now turned their attention to the Champions League for Tuesday night's match against Spartak Moscow.