Salah, after being dropped for the Champions League win at Inter Milan for his outburst after Saturday's draw at Leeds, has been recalled for today's clash with Brighton.
"If Mohamed Salah's intention with his grumble in the huddle at Elland Road was to weaken Slot, he must now concede that his misguided actions have had the opposite effect," Carragher wrote in his column for the Telegraph.
"The chief reason for Salah's miscalculation is his failure to fully understand the psychology of the club's hardcore fanbase. In a choice between a title-winning Anfield manager and a multi-title-winning footballer, the coach wins every time."
On being slammed by Salah's Egypt teammates, Carragher went on: "I couldn't care less, because I intuitively know I am on the same page as those supporters who were at San Siro on Tuesday night.
"I am in touch with enough of them to be able to measure if my mood reflects theirs. The day I no longer believe that to be true is the day I stop commenting on Liverpool."