Carragher's call follows Virgil van Dijk's statement that Liverpool are a 'mess' after their 3-0 defeat to Nottingham Forest, marking their sixth loss in seven Premier League games.
Van Dijk had urged his teammates to be 'angry' and labelled their performances 'unacceptable'.
Carragher questioned why Salah, who was vocal about his contract situation last season, is not showing similar urgency now as a team leader.
He suggested Salah only speaks out when he receives man of the match awards or needs a new contract, contrasting this with the need for other players to speak for the club.