New Zealand were excellent in a brisk opening to the game in which they turned pressure into points to lead 17-0, and two late tries secured a bonus point which probably ties up the Rugby Championship trophy for the All Blacks.
"The start was not idea for us, the first 20 minutes we struggled to get into the game because of poor discipline. I think we gave away four consecutive penalties," Nienaber told reporters.
"We made a lot of mistakes and those errors put us under pressure. The quality side that New Zealand are, they were able to capitalise and we had to play catch-up rugby for the rest of the game."
Nienaber said his side had expected New Zealand to come hard at them in the opening quarter.
"It is similar to what they did against Argentina, and on their end of year tour (last November), so we knew it was coming, we just couldn’t handle it," he said.
Nienaber conceded there were lessons to be learnt ahead of his team's Rugby World Cup title defence in France starting in September.
"We can’t start like that, with that many penalties and errors. Some of them were unforced from our side, but others were from the pressure they exerted on us. You can’t play catch-up rugby when you get to the World Cup," he said.
"I am proud of the guys with the way they came back, but we let it slip in the first 20 minutes."
South Africa captain Eben Etzebeth led the side despite the death of his father on Tuesday.
"I am not walking in his shoes, so I don’t know where he is at mentally," Nienaber said. "All we could do was support him as much as we can. He is a brilliant guy and it shows how much the Springboks mean to him."