Ireland ended their 111-year wait for a victory over New Zealand in the US, cutting short the back-to-back world champions' record winning streak at 18 matches.

Hansen also admitted the New Zealand Rugby Union (NZRU) had worked hard to prise Schmidt away from Ireland and back into their Super Rugby coaching set-up.

"He's probably one of the best coaches around," said Hansen of Ireland boss Schmidt.

"He's meticulous in his work ethic, a good analyst of the game and that's why Ireland want to keep him and why New Zealand wanted to bring him home."

Schmidt only signed his new Ireland contract two weeks ago, committing his future to the Irish Rugby Football Union (IRFU) until after the 2019 World Cup.

The 51-year-old had seriously considered taking a coaching job with either the Highlanders or the Chiefs, but eventually opted to remain in Dublin.

Family concerns and the desire to lead Ireland past the quarter-finals of a World Cup for the first time tipped the balance in the end, however.

Schmidt has already assured his place in Irish folklore courtesy of Saturday's victory, whatever happens next, but New Zealand coach Hansen expects his countryman to continue to guide Ireland on an upward curve.

Hansen believes Schmidt can rightly be viewed among the sport's shrewdest minds, after adding the maiden All Blacks scalp to Ireland's first win over the Springboks on South African soil in June.

"It's good for Joe, and Joe's a really good man, I've got a lot of time for him as all our coaching staff has; he's a top bloke," said Hansen of Schmidt.

"He's working hard and trying to do something with Ireland and he's having some success.

"They're having a great year, they've knocked over South Africa and they've knocked us over. So he'll be feeling pretty pleased with himself and so he should.

"He's done a good job with them and the rest of his crew are supporting him.

"So I don't think there's any big significance.

"Some people will get excited about it I suppose but it doesn't make any difference to us who it is.

"You don't like losing at the best of times but in saying that you have to accept it.

"Thankfully we get another opportunity in a couple of weeks' time and we'll see if we're good enough then."

Captain Kieran Read had admitted ahead of Saturday's Chicago showdown that the 2016 All Blacks were desperate not to be the first New Zealand side to lose to Ireland.

But in the wake of that unwanted moniker, Hansen insisted the tag would not act as any kind of millstone.

New Zealand take on Italy in Rome on Saturday, before facing Ireland again in Dublin on November 19 - with Hansen already eyeing the chance to set events straight from an All Blacks perspective.

"This team's about history, it's made a lot of positive history and it's still making history," said Hansen.

"Ireland played better than we did and deserved to win.

"When you look through the ages, (at) Christchurch they probably should have won, Dublin they should have won, so they've come out this time and won the game.

"So I don't think it's going to be something that hangs around our necks and strangles us to death that we've lost to a good Ireland side.

"What we've got to fix is the issues in our game.

"The challenge for this group now is to do that, to get themselves up off the floor and have a good look in the mirror at ourselves, coaches included.

"And then it's to find out what we can do that we didn't do right, and front up against Italy, and then Ireland and France and finish the season off on a good note."