"I think we did enough to win the game, there were just two points needed for us to get over the line", said Coetzee.
They twice held the lead in the second half only to be pegged back by the world champions, with a converted try from Malcolm Marx in the closing stages leaving South Africa agonisingly short at the final whistle.
Hansen said he expected a backlash from the Springboks, who were heavily criticised by their fans after their record defeat at North Harbour Stadium. "In that game we took every opportunity, and tonight we didn't", he said.
"In both matches against Australia we were in it and could have won it, but did not".
"57-0 is much easier on the ticker".
"I'm really proud for a young team that we have been able to grow and to get the win".
The team suffered a first loss on home soil this year when they were edged 25-24 by the All Blacks, who finished the Rugby Championship undefeated and retained the title they won in 2016.
The champs also came through after losing playmaker Beauden Barrett to a head knock midway through the first half, and unsafe winger Nehe Milner-Skudder to a dislocated right shoulder at the end of the half.
New Zealand: 15 Damian McKenzie, 14 Nehe Milner-Skudder, 13 Ryan Crotty, 12 Sonny Bill Williams, 11 Rieko Ioane, 10 Beauden Barrett, 9 Aaron Smith; 1 Kane Hames, 2 Dane Coles, 3 Nepo Laulala, 4 Sam Whitelock, 5 Scott Barrett, 6 Liam Squire, 7 Sam Cane, 8 Kieran Read (c).
File: New Zealand All Blacks vs South Africa Springboks - Auckland, New Zealand - September 16, 2017 New Zealand's Anton Lienert-Brown runs through South African defence.
The second came when De Allende followed through after attempting to charge down a Sopoaga kick, and made contact with the flyhalf late and high.
"Some of our younger players have not been in that situation before - that when it is tough you have to find a way".