The Toffees played more than 30 minutes at a man disadvantage after Steven Pienaar was sent off for a second bookable offence.
Neville thinks that some spirited rearguard action in the closing stages proves that his team are able to grind out results under difficult circumstances.
He told Sky Sports News: "I think we can play better but I think today we showed other qualities.
"Today was always going to be a game where our centre-backs were so important, and the two centre-backs and two full-backs were rocks today.
"It's probably the first time this season we've really had to dig in and sacrifice a lot of our attacking play so we go into next week's derby full of confidence."