Salah drew a blank in Sunday's defeat at home to Manchester United on Sunday.
Carragher told Sky Sports: "I don't think Salah should be like a Virgil van Dijk where it's like 'first name on the teamsheet'.
"Liverpool have got two away games - in the Champions League at Frankfurt and then they go to Brentford. I don't think Salah should start both of those games.
"He should always start at Anfield because Liverpool will be on top, around the edge of the box and more often than not he scores in those situations today.
"But I do think in the away games and helping your full-back, I don't think Salah should be starting every game right now, certainly away from home, with the form he's in."
Asked if Salah would accept not playing, Carragher replied: "Would he be OK with that? Probably not.
“But when you get to a certain age you have to understand that, especially when you're not playing well, where's your argument?
"It's different if you're banging in the goals and your manager makes a tactical decision and you're frustrated.
“I don't think Mo Salah's in any position to complain if he was left out of one of the next two away games."