"When you are No.1 in the world every team you play against is out for you, they are hunting for you," the skipper said.
"It takes a lot of hard work to stay at No.1.
"If it does happen ... we've got a pretty tough series in a couple of months' time in Sri Lanka.
"Lots of hard work still in us after this series."
Australia's previous stint at No.1 came in June 2014 but South Africa reclaimed the mantle a month later.
To reclaim top spot so soon after the retirements of Michael Clarke, Shane Watson, Mitchell Johnson, Ryan Harris, Chris Rogers and Brad Haddin would be an outstanding achievement.
"They are a big part of it, obviously the rankings keep on going and those guys were a big part of getting us where we want to get to," Smith said.
"We've got a pretty new side and guys are gelling well together.
"It's been really satisfying.
"There's still a lot of improvement left in us but I think we are going in the right direction."
NZ resumed at 178-4 on day four, their hopes of salvaging a draw having been all but dashed by the loss of key batsmen Kane Williamson and Brendon McCullum on day three.
Australia turned the screws despite Peter Siddle being restricted to fielding duties because of back spasms.
From the moment Josh Hazlewood grabbed three wickets in his opening spell on Friday, NZ's 13-Test undefeated streak at home looked in a degree of doubt.
Adam Voges scored 239 to be named man of the match, while Usman Khawaja and Smith delivered crucial knocks after their side slumped to 5-2 on day one.
It was 52 runs short of being the biggest margin for a trans-Tasman Test in NZ.
"We were completely outplayed," McCullum conceded, refusing to moan about Voges' no-ball reprieve on seven.
"Australia were excellent.
"We've always said we're not afraid of losing but we're going to try and make it difficult for the opposition to beat us. That's the most disappointing aspect."
Smith expected the Black Caps to hit back hard at Hagley Oval in McCullum's swansong.
"New Zealand are a very good cricket side," he said.
The 26-year-old was also hesitant to discuss the challenge of winning in England and India.
"It's extremely tough to win anywhere. So I won't put anywhere above, or any team above any other team." he said.
- AAP