Liverpool were 2-0 up after just 20 minutes, but Leon Osman pulled a goal back almost immediately before Steven Naismith's first goal for Everton secured a point.
Everton captain Neville, who was booked for diving in the first half, felt his side could have passed the ball better, but was prepared to accept a draw.
"I think when we were two-nil down we'd have took a draw but we got back into the game so quickly and we felt we had the momentum," Neville told Sky Sports.
"We maybe should have passed it a little bit better, took that extra touch. I think we needed control of the game in the wide areas.
"These games are fast and furious and you go home later and you analyse whether it was an offside goal.
"We also had chances to score so maybe both teams are happy with a draw in the end."
Naismith's strike was his first since his move from Rangers over the summer and it was also his first goal since coming back from a cruciate ligament injury sustained in October last year.
"It's been a year since my last goal," said the Scot.
"I'm glad just to start and to get a goal was nice as well."