They lost to France, but restored their pride with an excellent 43.495s, a national record.
"To produce a national record and fifth at our first Olympics is pretty bloody good now," Dawkins said.
They have better days ahead. The sprint programme is still in its infancy and this group has always had Rio de Janeiro as the end goal. Their bronze at the recent world championships hinted at a chance for a medal, but they were aided in Melbourne by Great Britain and France being disqualified for changeover infractions.
New Zealand's men's team pursuit was also in action this morning, riding a qualifying time of 3m 57.608s. It wasn't brilliant, but it was good enough for third leading into tomorrow's action.
They will ride-off against Australia. Win and they're almost certainly in the gold medal ride-off; lose and there's still a good chance they will be in a ride-off for bronze, probably against Denmark or Russia.
"The next round is all or nothing," Bewley said. "It's just a race against another team. If you want to make the gold medal ride-off, all you have to do is win. It doesn't really matter what time you ride as long as you are fast enough to make the bronze ride-off."
Bewley said they had got a few small things wrong during their ride and could probably trim a couple of seconds off their time.
"We definitely didn't ride as fast and as well as we wanted to. The way we wanted to execute the ride was a little different to that. Looking at the Aussie team, it's probably the same situation in their camp.
"It's two teams who are capable of going much quicker in the next round."
The opening night at the velodrome was dominated by the twin powers of Great Britain and Controversy.
Their men's sprint team of Philip Hindes, Jason Kenny and Sir Chris Hoy blitzed opposition, winning the final in world record time of 42.600s. France was second and Germany third.
Britain's team pursuit also looks unstoppable, having set a world record time 3m 52.499s.
The women's sprint team, including glamour girl Victoria Pendleton, missed out on the final, despite setting a world record in qualifying. They were disqualified for an early change.
In the final, the Chinese team of Jinjie Gong and Shuang Guo, by now world-recordholders themselves, were first across the line but also relegated by the commissaires.
That opened the door for the German duo of Miriam Welte and Kristina Vogel to pinch gold, with Australia third.