The Toffees showed fight and vigour to claim a point, scoring two goals in 14 first-half minutes to tie the game after falling behind early on through a Leighton Baines own goal and Luis Suarez's smart finish.
And, despite admitting the team would have been happy with a draw after the Uruguayan netted Liverpool's second, the midfielder acknowledged that his team must start winning games if they are to compete for Champions League qualification come the end of the season.
"We want to stay in the top four," Neville told Sky Sports. "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."
Neville was booked during the first half for falling to the ground under little-to-no contact from Daniel Agger and revealed manager David Moyes – who spoke out against Luis Suarez with regards to simulation ahead of the game – showed him up in front of his team-mates at half-time.
"It was an absolutely stupid thing to do," he admitted. "I don't find myself in that situation [near the opposition goal] very often and I thought Daniel Agger was going to take me out.
"I, rightly, got a good kick up the backside [from Moyes] at half-time and was given a yellow card which meant I couldn't commit into tackles in the second half. I won't do it again, that’s for sure."