"I think it did," Punt said. "But leading into this tournament we'd get the lead and we'd drop off and let them back in. It was a really good effort in defence.
"We haven't held a 1-0 lead for a long time. It was really hot out there, it was hard."
Punt's blinding pace caused Australia's defence issues, but they were not able to capitalise on this often enough, much to the frustration of both coach and player.
"You could probably hear the coaches' yelling at us," Punt said. "One of our strengths is our speed. We need to round the outside more and look for options. We need to look at that against South Africa."
Punt is expecting another hard fight against South Africa, saying when New Zealand does win against them, it tends to be by the barest of margins.
New Zealand have been handed a brutal pool. They must win their next match before they face the No 2-ranked team, Argentina, on Friday morning (NZT). The sixth-ranked New Zealanders then have a date with the 10th-ranked US, before rounding out pool play with another tough game against Germany (No 3), who beat them 5-1 in a pre-Olympic international.