"I thought 183 wasn't too bad, but the wicket dried out quicker than we were hoping for. In hindsight, if we could have got 250 we would have been in the game. I think today the ball was starting to turn a bit and reverse swing as well, because of the abrasive nature of the surface.
"Their bowling was world class. It wasn't just in the first innings but the way they went about the second innings on that wicket. They quickly identified the ball wasn't swinging conventionally. Once the ball's reversing it's another thing to apply pressure and execute it. It's not a reinvent the wheel situation but we've got to tidy up a few areas.
"Take Josh Hazlewood. He's developed really quickly. He was probably the junior member of the line-up six to eight months ago. He's an excellent bowler who has made adjustments in different conditions to get some good results. He will be a guy who, when we turn up at Hagley, we need to find a method to keep him out of the game. At the moment he's proving dangerous."
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Smith was pleased they responded overseas after struggling in the Ashes. He said they relied on reverse swing today.
"It is a conscious effort [to prepare the ball]. It doesn't work out every day. There were a couple of [used] wickets either side of the block where you could get the ball into and we got lucky. Someone hit a cut shot and it really scuffed one side, so that got it started for us. I thought once we got the ball to go we executed well by putting it into good areas. We built pressure and the bowlers reaped the rewards.
"With our batting we got through the tough periods, Adam Voges did that beautifully on the second morning. It was quite tough for him but things got easier."
Both captains downplayed the Richard Illingworth umpiring error when he called an incorrect no-ball when Doug Bracewell bowled Voges on seven.
""Everyone makes mistakes," McCullum said. "You've got to be careful it's not knee jerk. It's unfortunate for him that it probably had a bit of a bearing on the game. But we had our opportunities to rectify it and we didn't do it."
"Everyone makes mistakes, whether you're a player or umpire," Smith said. "Hopefully they can find a way to resolve that so those sort of mistakes don't happen too much in the future."
McCullum believed they still had the capability to beat Australia, despite losing three of four tests this summer.
"Over the last while we've always said we're not afraid of losing, but we're going to make it difficult for the opposition to beat us.
"That's the most disappointing aspect of this, we weren't in the game for as long as we wanted to be.
"[From a personal perspective innings of] 0 and 10 are not ideal. You come into the game with huge expectations and you want to do well. Sometimes the game doesn't marry up to the ambitions that you have, but I'm really excited about that last test."
"We got in front of the game, and didn't let them back in at any point," Smith added.
Australian fast bowler James Pattinson looks set for a recall in Christchurch, especially if Peter Siddle's back spasms continue.
A decision on Ross Taylor's fitness is due out later today.
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