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Departed coach Steve Hansen has called on All Black supporters to back Foster and his new team.
In a lengthy interview with Newstalk ZB's Martin Devlin, Hansen said the 2007 World Cup quarterfinal defeat to France and the drawn series with the British and Irish Lions two years ago remain his greatest disappointments.
He is extremely proud of his record and said the 2019 semifinal defeat against England would "not define myself".
But Hansen was clearly aware that Foster, his longtime assistant, is lacking anything close to universal support among fans, many of whom supported the Crusaders' title-winning coach Scott Robertson.
"It's time to sit back and let him (Foster) take over and enjoy watching without all the pressure that comes with being the coach," Hansen said.
"Yeah I'm happy (with Foster's appointment)...look I think we had two outstanding candidates. Scott Robertson is a very, very good coach in his own right and could well have done very good too.
"Fozzie is also a very good coach in his own right, and probably a coach at the moment who a lot of people aren't giving the respect he probably deserves, because he is a very good coach.
"He's not the coach a lot of people thought he was 10 years ago. None of us are.
"The important thing I think now is everybody who supports the All Blacks gets in behind him. I think back to my time when I took over from Ted (Graham Henry), a lot of people thought I didn't deserve to get the job. You've got to give people an opportunity.
"They've decided Fozzie is the man to do the job we've all got to get in behind them and support them."
Hansen's advice to Foster was: "Be yourself, you're good enough, trust your own instincts because they're good."
On other matters, Hansen said New Zealand rugby could not become complacent about player development, saying the quality production line was under threat.
"The biggest thing we've got to work on is our underage development because there are so many people wanting our players," he said.
"It's getting harder and harder as the game gets more and more professional to keep them here in NZ. The money is very hard to compete with and we don't have a lot of.
"We have a nursery of good players and everyone comes here for the players, just like they do for the coaches. We've seen a number of coaches snapped up as well.
"There's plenty of talent, we've just got to make sure we don't get too confident about it, and think that it's always going to be there. We've got to keep working hard at developing it."
He blamed travel fatigue for the All Blacks' increased struggles on northern hemisphere tours, saying: "We go around the world twice…seven tests in nine weeks is fatiguing. We've dropped games up there in recent times because we've just been hanging in from a fatigue point of view.
"If we want true global game…if we want the Super Rugby champions to play the European champions, the Six Nations champions to play our four nations champions, we've got to find time in the windows.
"We have to invent better ways particularly in the in southern hemisphere, cutting down some of the travel. Some of our governing bodies have to look at what they are doing."
Hansen said the 2019 World Cup defeat to England was "still painful" but the rest of the tournament was pretty good and there could be no complaints about the semifinal loss.
"I think '07 (when he was Graham Henry's World Cup assistant) is still the most disappointing," he said.
"I was pretty disappointed with the Lions, the way that went down, to draw a game in final test, with a pretty average (refereeing) decision made at the end. You want a clear-cut result, but whenever you lose it is disappointing."
And don't expect Steve Hansen to critique his All Black successors.
"The job is hard enough without having former All Black coaches or former All Black players dishing dirt on how the team is going," said Hansen, who has a short-term coaching role with Toyota in Japan.
"You've just got to give people space to do their job and understand when you've been there yourself you know how hard it is.
"We've got a good man who has taken over, he'll surround himself with good people I'm sure, we'll let him get on the job and I'm sure we'll get great results."