Smith and his men ruthlessly dominated the three-test home series against West Indies, winning it 2-0 after the rain-hit final match ended in a draw in Sydney on Thursday.
"We've always played quite well at home but the challenge for us is to make sure we're winning series away from home, and that starts with a tough series for us in New Zealand," Smith said.
After this month's limited over home series against India, Australia tour New Zealand and Smith warned the conditions would be difference across the Tasman.
"Hopefully we can adapt to the conditions we’re going to face in New Zealand," Smith said.
"I daresay they’re going to have a bit of grass on them and are going to swing a bit. So we have to be better than we have been previously on those sort of wickets and hopefully we can adapt well and have a successful tour there."
Victory in New Zealand, provided England translate their 1-0 lead in the ongoing four-match series in South Africa into series victory, will see Australia return to the top of the test rankings.
Smith had no doubt his team mates would adapt to the conditions to achieve top rankings.
"I've had a few chats about it to some of the boys. When you’re under pressure you go back to the way you know and that can hurt you a little bit away from home.
"I think you almost have to find another way to do things. Whether that be playing in England or New Zealand making sure you play under your eyes. Here you can play out in front of you a little bit more but that will get you into trouble in England and New Zealand."
(Reporting by Amlan Chakraborty in New Delhi; editing by Patrick Johnston)
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