Ireland has never made it past the quarterfinals at a World Cup, and despite being the No1 side in the world in 2019, the All Blacks hammered them 46–14 in the quarterfinals.
In the wake of Saturday's fourth Grand Slam achieved by the side, Best told The Irish Times, "The first thing is to enjoy where they are right now. Grand Slam champions don't come around very often."
It was no secret what the next challenge was, and Best said there was no harm in talking openly about how and why Ireland could win in France.
"Out from 2019, we could always say we realistically had a chance. The difference with this team is they're showing a level of consistency and depth. Before, there was a little more reliance on two or three players playing in form.
"Whereas with this team, if someone is not playing well, it seems there's two or three behind them who can step in. You can also pick the form player, and not feel you're weakening the team on the team sheet."
The Six Nations win over England at the weekend showed Ireland could deliver under pressure.
"What impressed me, and the difference compared to other teams, is that they can always find another gear.
"Before, when we struggled, we struggled the whole way through and invariably lost some of those games.
"This team, even when they're now playing the best rugby, find a pocket of time during the game where they just find another gear, drive the game away from you.
"That reminds you of the brilliant New Zealand teams.
"Once they go more than a score ahead, you feel it's over, and that's what the best teams in the world have."
Best said working in commentary with World Cup-winning coach Sir Clive Woodward told him that if England were in Ireland's position, they would already be discussing winning the World Cup. But, having beaten the top three teams in the world, New Zealand, South Africa and France, they had the form to do that.
"You have to understand how we got here, the last 24 months especially, and how to keep getting better.
"To win the World Cup you need depth, which we have, but, ultimately, you need players in form, and that's where we fell down four years ago, too many players fell out of form."