A week after beating the Springboks 24-17 at Eden Park, the home side crashed to their worst-ever test loss on Saturday as the visitors piled on 36 unanswered points at Wellington Regional Stadium.
Lock Barrett, part of a forward pack that was well beaten on the night, said the sting of the defeat would not fade quickly over the two weeks before meeting the Wallabies.
"There’ll be some real discomfort this week," he told reporters.
"But I’m sure this team will use that to bounce forward. We’ve got the Bledisloe ahead and a chance to respond."
New Zealand's final two tests of the Rugby Championship double as the Bledisloe Cup, the annual trans-Tasman series contested with Australia.
The Wallabies, who were beaten 28-26 by Argentina earlier on Saturday, lead the Rugby Championship with 11 points, one ahead of second-placed South Africa, the defending champions, and third-placed New Zealand.
Having beaten South Africa with a smart aerial game at Eden Park, All Blacks coach Scott Robertson said his team failed to deal with their high balls in Wellington and repeatedly paid for it in the six tries-to-one rout.
"When they got rolling, they were relentless. We couldn’t buy a moment, and they punished us,” Robertson said.
"They’ve been criticised for it in the past, but they own that space now. They put pressure on us, and it worked."
Following the All Blacks' first-ever test loss in Argentina against the Pumas, the Wellington humiliation will put further pressure on Robertson and his staff over the direction of the team midway through the World Cup cycle.
Former All Blacks fullback Mils Muliaina was scathing in commentary on Sky Sport, accusing Robertson's men of almost giving up when South Africa ran riot late in the second half.
"It's not really the sight you want to see from the All Blacks," he said.
While declining to blame his players, Robertson said the entire group needed to take responsibility for the setback before they could move forward.
"Firstly, (we need to) own it," he said. "Get some responsibility and find out what we need to fix.
"We're not going to be chasing too many things. We've got to be clear about what matters most to us on and off the field. Then get a plan and look forward to this next game."