The Toffees travel to Anfield on Sunday in what will be Sam Allardyce's third game in charge since taking over the Merseyside giants last week, with Everton failing to beat Liverpool away from home in 18 attempts.
Both sides are in action in European football prior to Sunday's game, with Everton going up against Apollon Limassol in the Europa League on Thursday night in Cyprus while Liverpool play host to Spartak Moscow on Wednesday.
Neville recalled travelling to the home of Everton's bitter rivals with fear following the club's previous results at Anfield, and called on Allardyce's squad to show none of that if they are to end such a dismal away record against Liverpool.
"They need to get that monkey off their back," Neville said. "There is a psychological problem with Everton at Anfield - Liverpool have definitely got one over on Everton.
"They need to go there and be brave - when I was captain we used to go there a little bit fearful of what we were going to do due to the results of previous meetings. This team this year must go there with no fear and go to win."
Everton come into the game rejuvenated following the appointment of Sam Allardyce, as he watched from the stands during the Toffees' 4-0 win over West Ham before masterminding a 2-0 victory over Huddersfield.
Allardyce will not be travelling to Cyprus with what is likely to be a weakened squad to face Limassol in a dead-rubber outing, with the local derby on Sunday taking precedence.
Three points for Everton could see them climb into ninth position in the Premier League table, if Newcastle can halt Leicester City's good run of form with a home win at St. James' Park.