David Moyes' side slipped to the foot of the Premier League table on Saturday following a 0-0 draw with Fulham.
They are the only side in the top flight yet to record a win this season, with just three points taken from their six fixtures so far.
Neville acknowledges that the situation is becoming increasingly perilous, but is adamant that his side can turn the corner.
The Toffees are notoriously slow starters and no-one at Goodison Park is getting overly concerned just yet.
Neville said: "You come off the field quite pleased with the performance and find you're bottom of the league, but if you don't win football matches it's where you deserve to be.
"When I joined the club five years ago we lost six of the first eight, including six on the trot. I couldn't see where the next win was coming from.
"I remember saying to Leon Osman, 'Do you think we'll go down?' He said, 'Don't worry. Everton are slow starters but the spirit will show through'.
"That comment has stayed with both of us ever since. The spirit now needs to shine through.
"We had qualified for the Champions League the previous season but that was a totally different kind of team - it was up-and-at-'em, in your faces. We have progressed from there.
"We have players who have played at World Cup finals. The quality needs to shine through now. It's time to stand up and be tough.
"That doesn't mean going out and kicking people, it means doing the right things all the time and winning football matches.
"There's no point feeling sorry for ourselves. We have to go to Birmingham next week and, at the moment, draws aren't good enough for us."
Source: Team Talk
Source: Team Talk