The Reds forward suggested that he is "probably more out than in" at Anfield as he awaits an extension to his deal that expires at the end of the season but Liverpool legend Carragher is angered by the saga taking the focus away from what is a vital week for Arne Slot's team.
The Sky Sports pundit said on 'Monday Night Football': "I must say I am very disappointed with Mo Salah. Liverpool have Real Madrid midweek [in the Champions League] and Man City at the weekend. That's the story right now.
"If he keeps putting comments out, his agent puts out cryptic messages, that is selfish. That is thinking about themselves and not the football club."
Salah, Virgil van Dijk and Trent Alexander-Arnold are all out of contract at the end of the season but Carragher insists that the main focus should be on the team's goal of winning the Premier League title rather than the futures of individual players.
He said: "The most important thing for Liverpool Football Club this season isn't the future of Mo Salah, Virgil van Dijk and Trent Alexander-Arnold. The most important thing is Liverpool winning the Premier League.
"I hope they don't feel like this club would fall apart if they left. Steven Gerrard left the club and the next manager won the Premier League. Graeme Souness left and Liverpool won the Double.
"Salah, would we miss him? Of course we would. But Liverpool will move on."