Neville said: "There is still so much for us to play for. In the Premier League and then in a fortnight when we play our next UEFA Cup tie. The competition for a place in Europe is as fierce as it has ever been.
"There are so many good teams in and around the top eight, and the manager has gone on record saying this is the most competitive season since the formation of the Premier League.
"But we are still very much in the mix and fully intend to stay there. We know the scale of the challenge and know it will not be easy to stay where we are.
"But despite the disappointment of not getting to Wembley, you can still see the confidence within the squad.
"Soon we will have our three players back from the African Nations Cup, things will get better and we do have the resolve."
The news of Liverpool's 1-0 defeat at West Ham produced the biggest cheer of the night at Goodison, but boss David Moyes prefers not to focus on the fortunes of the club's bitterest rivals.
He said: "There is certainly less pressure on us than on Liverpool now, because we are not expected to make the Champions League. When people talk of the top four they do not mention Everton but I would back my team against any of our rivals.
"For us to finish fourth would be outstanding, but I do not see any point talking about it until there is a month to go and we are still in a strong position."
He added: "I did not know Liverpool had lost until after the game, maybe people will think I should be overjoyed. Of course it helps us when they lose, but I do not want to get too carried away with the current situation. Come the end of the season we will see how things are."