The Toffees' skipper is looking forward to a semi-final date with Merseyside rivals Liverpool at Wembley but also hopes his side can maintain focus to finish well in the league
The defender has urged the players to keep their good form going as they look to finish the campaign strongly in the cup and Premier League.
The 35-year-old was fully aware a defeat on Tuesday would have had a disastrous effect on team morale for the rest of the season.
Neville told Everton's official website: "You can imagine the massive comedown if we had not got the result at Sunderland.
"We have to make sure we keep this momentum going because it is building into something special."
As well as the cup, Neville believes Everton can finish strongly in the league. The Toffees are two points behind Liverpool in ninth place.
And the former Manchester United man is looking forward to crucial games in an attempt to automatic European qualification through the league.
"We are in a pack now with our next five or six games against teams in and around us," he continued.
"If we can get maximum points we will open up a gap. I know we can qualify for Europe via the FA Cup but there is still a glimmer of hope we can do it through the league."
Neville believes the recent upturn in form is all down to confidence in the squad and belives they can still reach the top six.
He continued: "The quality we have in the team and with the confidence building there is no reason why we shouldn't be challenging for Europe through the league.
"The key thing is to keep the momentum going.
"And if we can go into that semi-final on the back of three good victories that will mean we are bang in form."
Everton face West Brom at Goodison Park on Saturday and will be looking to do the double over the Baggies after picking up a 1-0 win at the Hawthorns earlier in the season.