Neville's men lost ground in their bid for a top-four spot in the Barclays Premier League as they were held by Swansea in a goalless clash at Goodison Park.
The Merseysiders remain in a healthy fifth place but the result meant they missed the chance to gain ground on Tottenham while Chelsea pulled further away.
Yet with the Toffees traditionally strong in the second half of the season, Neville expects them to keep pushing.
The veteran skipper said: "We need to keep believing and thinking like that, it is the only way to be. We want to finish in the top four, and not just fourth. We want to catch Chelsea and Man City.
"We have got to keep aiming high, not waiting for teams to catch us up. We can't look behind us. We have got to be positive, look forward to the next games.
"Every game in the Premier League in the next month or two is going to be really difficult. It is that time of year, the pitches are getting softer, a bit bobblier and the weather is cold.
"It is about digging out results rather than playing fantastic football. This was a disappointing draw but we live to fight another day."
- Sports & Recreation
- Barclays Premier League