Smith was fined 30 percent of his match fee late last night for dissent over his involvement in the Josh Hazlewood incident, when both Australians expressed their anger over the denial of an lbw appeal against Kane Williamson just before lunch on day three of the second test at Hagley Oval.
The seamer was hit for 15 percent of his match fee; Smith's was double presumably as captain more would have been expected of him.
"Yesterday was a mistake on my behalf and I've been hit with a code of conduct (charge) because of it.
"To me it's about trying to learn from my mistakes and trying to get this team moving forward in the right direction and playing the good, aggressive brand of cricket that we play so well.
"We know that there'a a line there that we can't cross."
McCullum, meanwhile, believes Smith is already a good way into establishing the platform for how he wants his Australian team to play.
"I think the team plays slightly differently to what they have done previously.
"Most Australian teams play the way their leader is.
"If you look at Allan Border, Steve Waugh, Ricky Ponting, Michael Clarke, they always take on a slight twist.
"Under Steve Smith, we've seen a very similar thing. This series has been played in great spirits, I think, and the one back in Australia.
"I think Steve Smith has been a catalyst for that. 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."
And McCullum gave Smith an endorsement in the wake of the dissent row.
He said this Australian side go about their business differently from some of those in recent years.
"They probably skin the cat slightly differently.
"The majority of their focus is on positive play rather than necessarily some of the semantics of past eras.
"They go about their work in a nice manner and they play hard cricket but in the series that we've had, I don't think they've ever looked to step over the line."
