Italy striker Balotelli has scored only once in nine appearances since signing from AC Milan for 16 million pounds ($25.84 million) and has often cut a frustrated figure during a series of low-key displays.
His abject performance in a 3-2 win at the Premier League's bottom club Queens Park Rangers on Sunday proved to Carragher that he should not play when Liverpool face the European champions in Group B.
"He doesn't run around enough," Carragher, who made over 700 appearances in all competitions for Liverpool, told Sky Sports television.
"Against Real Madrid you've got to get that crowd going. You need to get back to the Liverpool of last year and that pressing. There's got to be an energy about Liverpool that we haven't seen; we've seen it once this season at Spurs.
"It's going on too long now and we can't keep waiting. It's a huge game and Liverpool have to get something from it. They can't have any passengers against Real Madrid."
Liverpool are yet to recreate the sparkling form that saw them finish second in the Premier League last season and are currently third in their group having suffered a shock defeat against Swiss champions FC Basel earlier this month.
In contrast, 10-times European champions Real have won five consecutive league matches and Carragher expects the Spanish visitors to see a lot of the ball.
The former defender, who won the Champions League with Liverpool in 2005, says manager Brendan Rodgers must play fleet-footed Raheem Sterling in favour of Balotelli to ensure the hosts stretch the game.
"I would put Raheem Sterling in there because he can run in behind and Liverpool may have to counter-attack a lot of the game. Madrid may have a lot of the ball," he said.
"Sterling can also press from the front. He doesn't have to play right up front and he can come back and help the midfield.
"I think they can [get something from the game], but it's how Brendan Rodgers sets up. You've got to get Anfield bouncing. There's got to be an energy and intensity about Liverpool."
