Hansen made the comment while in his early days as a pundit on the BBC highlights show Match of the Day in 1995 following United's 3-1 opening day defeat by Aston Villa.
Neville, who is about to start a career as a Match of the Day pundit, said Hansen's remark was used as a motivational tool to fire United towards a Premier League and FA Cup double.
Ten more league titles followed with the famous five of Phil and Gary Neville, Paul Scholes, David Beckham and Nicky Butt featuring in the majority of them along with Ryan Giggs who had already established himself in the team.
"It was devastating because when Alan Hansen spoke, people listened," Neville, a versatile midfielder and defender, told reporters at a screening of Match of the Day at 50, a documentary celebrating 50 years of Britain's most well-known sports show to be aired next Friday.
"He was probably the first pundit that had that effect on the nation. I actually believed him and if you rewind the time I think he would say the same again and I would say the same thing again because he was right.
"But he actually fuelled the challenge in front of us. I think that statement took us on to another level.
"Once it got to March or April, when you realised we were in the hunt, that statement became part of our motivation and our mantra. It was one of the things we were talking about, trying to shove it down their throats."
Neville, now hoping to forge a career as a pundit having been part of David Moyes' short-lived management team at United last season, said Hansen's gaff had helped the Scot become a household name in Britain.
"As a pundit you need to do one thing to elevate yourself to an iconic status and that was his," Neville said.
"I think it's probably one of the best statements he ever made for his own career. As a pundit now I think he was right.
"But I think he just under-estimated the quality of the young players coming in."
Hansen retired after 22 years as a Match of the Day pundit last season and says he has never regretted the remark.
"The thing I got wrong was that those five United kids were superstars," Hansen said. "They went on to become greats.
"You will never have five come through like that again.
"As a pundit if you are going to be right be right, but if you are going to be wrong, be dramatically wrong, there is no future in being marginally wrong."
Neville said he no plans to get back into management after what he called a tremendous learning curve at Old Trafford last season, preferring to watch United begin a new season under Dutchman Louis van Gaal.
He said the Dutchman has an easier job than Moyes.
"I think David almost had an impossible job," Neville, who was assistant to Moyes, said. "Van Gaal probably has an easier job because he's not following Sir Alex, because for 27 years that club was ingrained in Alex.
"He can come in with a clean slate and if he wants to train at 11 o'clock he can train at 11 o'clock. They have had that crossover period. Maybe it was never meant to happen."