Williams, who toured with the Lions in 2001, 2005 and 2009, now believes his countrymen have a genuine chance of beating the All Blacks this Saturday - something that he could never have imagined when he began his international career in 1996.
"I'm not afraid to admit - and I think a lot of players would say - that maybe in the past you'd go out and more or less just try to keep the score down against New Zealand because you had no chance of beating them," said Williams, ahead of Wales' first international of the autumn series.
"It was once in a blue moon you played New Zealand before and this aura came over that they were invincible, whereas now you play against them more regularly.
"Physically and mentally they were way ahead of us, but I think the gap has definitely shortened.
"They're still a world-class side, but I think we've improved a lot as a group, individually and collectively."
Wales haven't beaten New Zealand since former Lions hero Bleddyn Williams led them to victory in Cardiff in 1953 but there is plenty of optimism surrounding the current crop of stars.
Having been in the Wales side that came within a point of the All Blacks in 2004, Williams played a key role in last year's Millennium Stadium encounter when Wales led 9-6 at half-time only to fall away in the second 40 minutes.
"A lot of the belief just comes with playing them more often. We're a lot fitter and stronger than we used to be and our structure is in place to help us try and beat these top sides.
"I think last year at half-time we genuinely believed we could go on but, full credit to them, they showed how good a side they were and outplayed us in the second half.
"So it's a mixture of things but we still haven't done it yet. It's great talking about it but we really need to try and win.
"You look at their team-sheet and it's Carter, McCaw, Nonu…world-class players in a world-class side. You never underestimate New Zealand. Perhaps they didn't have the success they would have liked and the country would have liked in the Tri-Nations.
"But they are still an unbelievable side and we are going to have to be right at the top of our game to beat them."