The 35-year-old admitted defeat in their midweek FA Cup quarter-final replay at Sunderland would probably have brought the campaign to a premature end.
But buoyed by the prospect of an all-Merseyside semi-final against Liverpool next month, Neville sees no reason why they cannot finish strongly, pick up a trophy and qualify for Europe.
"You can imagine the massive comedown if we had not got the result at Sunderland," he said.
"It could now be a great end to the season. Now it is about grasping what is in front of us and we have to show some real mettle.
"We have to make sure we keep this momentum going because it is building into something special."