Vettori's men are teetering, probably needing to win their remaining Super Eights stage matches, against defending champion Pakistan tomorrow and England on Tuesday, to advance to the semifinals.
It is a similar scenario to last year's Champions Trophy in which New Zealand found itself in sudden-death territory after losing its opening group match - also to South Africa - but bounced back with wins over Sri Lanka and England before beating Pakistan in the semifinals.
"I hope that sits well with us," Vettori said.
"We did it at the Champions Trophy, we had to win games on end. This is the same. It's opposition we've played a lot lately and we're pretty familiar with so we've got some confidence but they're going to be big games."
Vettori believes his team will be better for its experience at Kensington Oval, where the Pakistanis also lost yesterday, to England, and he thought there would be an improvement there tomorrow from a New Zealand side that was not far from its best against the big-hitting South Africans.
"In twenty/20 cricket you have to be perfect in your execution and we weren't that today," he said.
"It's the nature of the format that your four overs can be brilliant one day and pretty tough the next. We're hoping for a quick turnaround from some of the guys' performance today.
"Guys adapt pretty quickly, and hopefully one game out here will mean we're better for it in the next game against Pakistan."
Albie Morkel slammed 40 off 18 balls, including five sixes down the ground, to push South Africa out to an imposing 170 yesterday. He was supported by AB de Villiers (47 not out), Jacques Kallis (31) and Herschelle Gibbs (30).
Tim Southee was the most expensive New Zealander, conceding 39 runs off three overs, and his place could come under threat from Kyle Mills.
Vettori was happy enough with the bowling through the middle stages, including his own none for 21 off four, but said the game effectively swung in the last five overs, which cost 62 runs.
"We weren't as good as we normally are and it's a very small ground and if you've got a destructive hitter like Albie Morkel, it's a bad combination if you miss," he said.
"You can't get it perfect every time but there are certain situations within a game that you have to get right. Today it was the last four to five [overs]. It wasn't what I expected and wasn't what I want.
"We fought pretty hard [with the bat] but if we could do anything again, it would be doing that [death bowling] a bit better."
To reach 157 for seven in response against a quality South African attack on a slowish pitch left Vettori satisfied enough.
Nobody could go past opener Jesse Ryder's 33, leaving too much for the lower order to achieve, although Nathan McCullum again proved effective, scoring an unbeaten 26 off 17 balls.
South African captain Smith believed his side played "clever cricket and at a good intensity".
"We knew if we could set a good platform up front, it really allows the likes of AB and Albie an opportunity to score . . . their [72-run] partnership probably made the difference today."
