The Toffees were held to a 1-1 draw at Goodison Park on Saturday as Tim Cahill's header cancelled out Phil Bardsley's opener.
Neither side could gain the upper hand entering the final stages of a tight affair and Neville believes the tie is finely poised ahead of a replay at the Stadium of Light.
He told Sky Sports: "We are neck and neck in the league now, there is not much to choose between us.
"You speak to Sunderland, they will feel going back to their place they will be favourites.
"They probably are, but they will be wary of us. The pressure swings to them now.’’
The former Manchester United man also hailed the atmosphere during the clash on Merseyside and rued seeing his side miss a late chance to win it.
He added: "Their fans got behind them, it was a great atmosphere, but we are still in the hat and that is the most important thing.
"There weren't too many chances for us to win it - maybe we could have had a penalty, maybe not, then Johnny's header nearly won it.’’