Today's 2-2 scoreline with Merseyside rivals Liverpool means that the Toffees have now drawn their last three Premier League encounters.
Discussing his team's form, Neville has admitted that they are currently damaging their chances of finishing the campaign in a Champions League place.
"We want to stay in the top four," Neville told Sky Sports News. "We drew last week against QPR, we drew the week before against Wigan and we drew today. Draws aren't good enough. We need to win games. That's what Manchester City, Chelsea and Manchester United do.
"We are slightly disappointed with the last three draws we have had but it's about keeping the momentum going. We want to be in that top four [at the end of the season] and if we keep showing that kind of commitment and spirit we will be there, I'm sure of it.
"When we were 2-0 down we would have taken a draw but we got back into the game so quickly and we felt we had the momentum. In the second half we needed to control the game in the wide areas."
Everton are currently fifth in the Premier League table.