Smith said he will "cop it on the chin".
"I need to be better as a leader. I need to set the example and that wasn't good enough, I guess."
But the pride was apparent as he savoured the climb back to the top test ranking spot on the back of this series victory.
"It was a big motivation for us. I thought the guys adapted to the conditions really well and it's really pleasing," he said.
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Smith was unbeaten on 54 when the winning runs were hit in the seven-wicket victory - to back up his first-innings 138 - as Australia reached 201 for three.
New Zealand needed quick early wickets today and had a chance off the eighth ball of the day when Usman Khawaja edged Trent Boult between wicketkeeper and first slip.
Neil Wagner gave another wholehearted demonstration, bowling 12 overs of more short-pitched deliveries yesterday morning, and at one point chasing a ball off his own bowling to the deep mid-wicket boundary.
He repeatedly dug it in short to try to unsettle the Australian batsmen and create something and did it with his hand heavily bandaged because of a fracture below his left ring finger.
"You could see at the end he was out on his feet," outgoing skipper Brendon McCullum said. "He's not the most skilled cricketer that we have but, geez, it's hard to go past him in terms of his attitude."
But New Zealand could have few complaints and McCullum made clear, in the racing parlance he tends to adopt, that New Zealand "ran second" throughout the test and series.
He praised the quality of Australia's cricket, gave rival captain Smith a pat on the back and accepted that over the summer they were the better team.
"We went in well prepared with strong belief within the group and we tried to play the game in a way that's been successful for us, and we ran second."
McCullum accepted the lack of penetration from his seam bowling unit was a big factor in the outcome this summer.
"We found ourselves quite often bowling in the best batting conditions when the ball wasn't swinging and we weren't able to get reverse swing. Tim [Southee] and Trent, in particular, will be disappointed with their series. Sometimes everything can be in place but it doesn't work out."
New Zealand now turn to next month's world T20 in India. Test cricket is on the sideboard until a trip to Africa to face Zimbabwe and South Africa in August.
There will be a new captain and perhaps tinkerings in the way of doing things by then.
As for Australia, they can bask in a successful summer. McCullum is backing them for a long stint at No 1, based on their depth.
"That's the beauty of Australian cricket. They've got so much depth that, if they can get everyone heading in the same direction, and their game plans are simple, then they're going to be dangerous no matter what."