Australia won the Test by seven wickets to move to the top of the world rankings, but celebrations were marred by Smith being hauled before the International Cricket Council match referee to explain his actions.
He was charged with dissent in connection with the same obscenity-laden rant that cost Josh Hazlewood 15 percent of his match fee. The ICC was expected to announce Smith's penalty later Wednesday.
But Smith talked up the Australians as "nice guys" who play the game hard and push the boundaries but don't mean to offend.
Two of the more notable episodes are the notorious 1981 underarm delivery when New Zealand needed six off the last ball to tie an ODI, and in 2013, when then captain Michael Clarke warned England's Jimmy Anderson to prepare for a broken arm.
"I don't think we're not nice guys. We play a good, hard, aggressive brand of cricket," Smith said, admitting he and Hazlewood were wrong in how they approached the umpires after Australia were denied an lbw decision against Kane Williamson.
Smith said he believed at the time he was acting correctly to question the umpire's decision.
"I thought I was well within my rights to go up to the umpire and ask him why we didn't use the real time snicko," he said referring to the technology used to determine if the ball had hit the bat.
"For me it's about trying to learn from my mistakes and improve and try and get this team going forward in the right direction and playing the good aggressive brand of cricket that we play so well and know there's a line there that we can't cross."
Despite the on-field dissent, New Zealand captain Brendon McCullum, who retired from international cricket at the end of the Test, maintained there was a good relationship between the two sides.
"He plays the game for the right reasons as well. He plays with his heart on his sleeve but he's a very respectful guy and a wonderful cricketer.
"They're number one in the world now and a lot of that is to do with his leadership and (Australian coach) Darren Lehmann's as well.
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