Carragher has stated Salah's "legs are gone" after he was benched for the win at West Ham on Sunday.
Asked about the claims, former Bolton Wanderers manager Allardyce said on the No Tippy Tappy Football Podcast: "Stop it. He should know better.
"He should really know better. That's an absolutely pathetic statement, but he's good at them, isn't he?
"He's good at just throwing it out there for a bit of, you know, 'popularity'. To keep himself on the front end of it. That's a disgrace. His legs haven't gone.
"How can his legs go from what he did last year, having the summer off, and then his legs go this year? How can that happen? It doesn't happen overnight.
"How does he know anyway? He doesn't train with him, he doesn't watch him train. He sees him play, and he might not be doing so well, but that's like many of the Liverpool players."