Rain came to Australia's rescue when, after several interruptions, Friday's match was finally abandoned with Smith's men 53 for three off nine overs in pursuit of a revised victory target of 235 in 33.
But what most annoyed Smith was a profligate effort by his pace bowlers which allowed New Zealand to get off to a flyer.
The Blackcaps, for whom captain Kane Williamson led the way with exactly 100, were 254 for three in the 40th over and on course for a total well in excess of 300 following a dashing 65 from opener Luke Ronchi.
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But Williamson's run out sparked a slump that saw seven wickets lost for 37 runs in under six overs as New Zealand finished on 291 all out.
Josh Hazlewood did the bulk of the damage with six for 52 but his figures could not disguise poor returns for fellow quicks Mitchell Starc (none for 52) and Pat Cummins (one for 67).
"I thought it was probably one of the worst bowling displays that we've put on for a very long time," Smith said. "We bowled both sides of wicket. We gave them a lot of freebies. And it was pretty ordinary, to be honest with you."
This was left-armer Starc's first match since the second Test against India in March and Smith backed his spearhead to come good in their second match of the one-day international tournament against Bangladesh.
"Let's hope it's rust and let's hope it's gone," said Smith. "Because that was pretty ordinary. Credit to them they came out quite hard and played quite well up top and got their innings going. Kane timed his innings beautifully, played really well throughout the middle but we did not bowl well at all."
Smith accepted the weather had probably spared his side a damaging defeat, saying: "We still had a lot of work to do and they've got a quality bowling attack as well, so we perhaps got away with one there. We certainly would have preferred to be in New Zealand's position when we came off at the end."
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Tournament hosts England were the main beneficiaries after launching the competition with an eight-wicket win over Bangladesh at the Oval on Thursday.
Now one win against either of the trans-Tasman duo will see Group A leaders England into the semi-finals.
Australia and New Zealand collected a point apiece for the washout, although both teams knew before the tournament started they'd likely have to win at least two of their three group matches to reach the semi-finals.
"It's obviously not ideal for both sides to have a washout," said Smith. "For us now it's just about making sure that we're playing each game like a final and winning the next two."
Williamson, as calm off the field as he was on it, where his considered stroke-play was in marked contrast to much of the big-hitting around him, refused to be downhearted after the chance of a prize win over Australia was washed away.
"The guys were going well with the ball in hand and it would have been interesting to see how it unfolded but we can't control the weather," he said. "We thought today was pretty good, and it's important we move on to the next game (against England in Cardiff on Tuesday). The nature of this tournament is every game is basically knockout-style. We'll need to be better again going into the game against England."
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