New Zealand's woes were compounded on Tuesday by an injury to Daryl Tuffey which could rule him out of the World Twenty20 next month.
The Black Caps suffered a ten-wicket defeat against Australia in Wellington in the first Test, and they will make at least one change for the next Test due to Tuffey breaking his hand whilst batting.
Tuffey will undergo surgery on Thursday to repair a broken metacarpal bone in his left hand and faces a race against time to be fit for the World Twenty20 in the West Indies which begins next month.
"He's a guy who has been pretty consistent for us since he's come back into the team," said captain Daniel Vettori.
"He didn't take the wickets in this game that he would have liked but I think he bowled relatively well. He knows the Hamilton conditions well so he is a loss for us."
Australia dominated at the Basin Reserve and Vettori acknowledged that taking just five wickets in the match is nowhere near good enough.
"Having them 176-4 and not kicking on from there (was costly)," he said. "If we'd been able to take wickets and break that (Michael Clarke-Marcus North) partnership (of 253) then that could really have changed the game.
"But you need to take 20 wickets to win a Test match and we only got a quarter of the way through. We obviously need to lift a lot, particularly the first-innings efforts.
"We fought hard in that second innings but we need to show more penetration with the ball in that first innings and stand up more with the bat. We can't afford to be on the back foot at any stage against Australia in Hamilton."
Aussie skipper Ricky Ponting paid tribute to Clarke (168) and North (112) after their record sixth-wicket partnership in the first innings set up the victory.
Clarke and North entered the match under intense scrutiny - Clarke due to the highly-publicised break-up with model Lara Bingle and North because of poor form.
"A lot of our players tend to react and respond really well when that sort of stuff is hanging over their heads," said Ponting.
"It's great to see the guys that worked as hard as they did leading into the game get the reward that they did in the game. There's no doubt their partnership in the game was a big reason why we're sitting here with a 10-wicket win on day five."
Ponting said he never had any doubts about the timing of the declaration or the victory, despite New Zealand's stubborn second innings batting.
"The declaration had a lot to do with the weather I knew was coming (on day four)," he explained.
"We could have batted and got 600 or whatever we wanted to. But by doing that and losing the majority of the day yesterday it would have been touch and go whether or not we would have got a result in the game.
"For me and the Australian team it's all about giving ourselves the best chance of winning so I felt pulling out at that time and even enforcing the follow-on when we did was giving ourselves the best chance to win the game."