The Boks were in stunning form last Friday against their old rivals with captain Siya Kolisi among the try-scorers in a 35-7 victory but, as Nienaber pointed out, that win came on the back of a 35-20 win for the All Blacks in Auckland in July.
"Four, five weeks ago in the Rugby Championship New Zealand had quite a good result against us, this time it was different," Nienaber told an online press conference from the team's training base in Corsica.
"If you are off by one percent then teams can put you away.
"So you have to be consistently 100 percent ready. If you're off slightly then top teams can put you to the sword.
"There are a lot of teams that are in a position to win the World Cup so in terms of that it is probably the most tightly-contested World Cup in history."
If it is too tight to call a favourite, Nienaber knows that the Boks have a target on their backs following their victory over England in the final in Yokohama four years ago.
"We knew we were coming as defending champions, you can't shrug that off, it is what it is. We are comfortable with that," he said.
It is a different story to four years ago when Nienaber joined up with director of rugby Rassie Erasmus to deliver that 2019 title.
"The main thing is when we started in 2018 there was limited time in getting prepared," said Nienaber.
"This time around we had four years although one year was taken away due to Covid.
"Our aim has been to get a strong squad together, try to create squad depth and that’s probably the difference."
South Africa begin their Pool B campaign on September 10 against a Scotland side that came third in the Six Nations and beat France during their warm-up games in Edinburgh.
Nienaber said the Corsica training camp had allowed his players "one last top up in terms of conditioning" before going into the World Cup.
"But we have had one eye on Scotland," he said.
"Scotland are quite a fit team and they can get stuck in and play their game, which they are very comfortable with, until the 85th minute.
"They also have solid set pieces. To play with rhythm and play the ball wide you need solid set pieces."