Salah was left on the bench by manager Arne Slot and spoke to a gaggle of journalists afterwards, admitting he had "no relationship" with his coach and that someone is trying to force him out of the club.
"Knock on the manager's door, see the owners, whatever you have to do, express your frustration," Murphy said on Match of the Day.
"By doing this, he's causing the team a problem and the manager a problem and making it all about him.
"You can't do it. Whether you agree with him you don't deal with it like this.
"Everyone has to fight for their place and perform at a certain level.
"A lot of other big-name players are getting stick and getting the fanbase turned against them a bit. Everyone is being judged."
Murphy added: "I hope it doesn't end badly because of everything he's given but there's always a chance if he's adamant.
"Liverpool are in charge of what happens because they have got his contract. But if he's adamant he wants to leave, maybe we'll see something in January."