Neville wrote in his column for the Daily Mail: "A championship-winning team has to have endurance of the mind, focus and concentration across the whole season.
"Kenny Dalglish is an experienced football man who has won league titles himself as a player and a manager.
"My guess is he will be looking very closely at his players over the next few months, to see which of them change their mentality from a big match to a small match.
"They're the ones that are the danger, the ones that celebrate after big games thinking the job is done, only to drop points in the next game.
"They're the players you have to weed out. That's what Sir Alex Ferguson has done for 20 years.
"When he feels that players aren't at the same level any more, that losing doesn't hurt them as much or that they aren't preparing the same way, he will get rid of them.
"Any little weakness is eliminated, because you need strength of character in the dressing room.
"Liverpool need to develop that mentality now."