United ended the season without a trophy, after losing the Premier League title to bitter rivals Manchester City in the closing minutes of the campaign.
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Neville believes that the Old Trafford side will have more to prove this season, and there will be an extra incentive to put things right.
"The challenge this season is always the same," Neville told the club's official website. "It's to win the Premier League, do well in the cups and do well in the Champions League.
"That challenge never changes. But, obviously, when you don’t win anything you have an added incentive because people start to question the team and wonder if the empire is crumbling.
"United now have an opportunity to put things right.
"The manager and the players have had to cope with all that before. So this challenge is something they'll all be looking forward to.
"You can bet they would have had a frustrating summer, though, after not winning any trophies last season.
"The beauty of football is that you start a fresh each year with a clean slate."