The former captain has transitioned from head coach of the axed Moana Pasifika to act as defence coach under new All Blacks mentor Dave Rennie.
Still disappointed by their 3-1 series loss to South Africa, New Zealand will look to vent their frustrations in Saturday's Eden Park Bledisloe Cup opener in Auckland.
"That sticks in the guts a bit; we have to come out with a response after that," Umaga said.
"There should be no hesitation around understanding what this weekend means to us."
Umaga was a key figure when the All Blacks halted the Wallabies' five-year Cup run in 2003 and New Zealand haven't lost a series since.
"That was my expectation," he said of their long grip on "Bleddie".
Umaga won two series as captain but the scars of previous losses remain, including in 2000 when the Wallabies pinched two late lineouts and John Eales kicked the match-winner well into injury time in Wellington.
"I was part of the team that won it back. It took us a couple of goes and some were quite heartbreaking, the ones we lost," he said.
"I've shared that with the group; what the Cup means to us, the people that have played and coached for it and what's happened to those people.
"It's up to them now to stake their claim."
Victory at Eden Park would make it 25 consecutive Test wins against the Wallabies at the venue since Australia's last victory there in 1986.
New Zealand haven't lost to any Test nation at the Auckland stadium since 1994, their run now an incredible 53 Tests.
The Springboks were able to leverage their set piece dominance to pile on 33, 29 and 43 points in their recent wins over the All Blacks, who won the first game 33-16.
Umaga expects the Wallabies - who haven't won a Test in New Zealand since 2001 - to play more expansively, and is wary of a side that's scored at least 26 points in all eight Tests played this year.
They amassed 42 in a last-start win over the Springboks in Perth, and it could have been more if not for four yellow cards late on.
"They're playing with more width and having numbers across the field," Umaga noted of the changes in attack under new coach Les Kiss.
"You can see the stamp of Les Kiss on this Wallabies side. And you've got to think that's a positive with the way they've been playing.
"We have to make sure we have the answers to the questions they pose."
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