He said he still feels the suspensions handed to Smith and Warner — which will see the pair miss the entire 2018-19 summer of cricket in Australia — were overly harsh.
"I'm not sure there were team culture problems … but I have noticed there is a lot of whingeing coming out of the Australian camp in recent times, about the opposition and things like that," Warne said.
"I think that's un-Australian, I have never really heard any Australian sides do that.
"But I think it's a great opportunity for everyone in world cricket to draw a line in the sand and say "how do we want to play the game?", "what do we stand for?", "what's the style of play we want?".
"I don't think we want to play like the Kiwis, which I heard someone say. I mean c'mon. The Kiwis, no thank you.
"But we probably want something in between the Kiwis and Australia at the moment. I want us to play hard but fair, tough, uncompromising cricket, but shake hands and play in the spirit of the game and show good sportsmanship."
Former coach Darren Lehmann said before his resignation that he supports the idea of changing the Australian cricket team's culture to follow the Kiwis' example.
"The thing for me would be if we take a leaf out of someone like, say, New Zealand's book in the way they play and respect the opposition," Lehmann said in Johannesburg before the Fourth Test against South Africa.
"We've got to make sure we're respecting the game and its traditions."
Warne's confirmed move to Fox Sports adds tremendous star power to the pay TV network's plans to "revolutionise" cricket television in Australia.
Warne, who has been part of Nine's cricket coverage for years, will join Big Bash stalwarts Adam Gilchrist and Mark Waugh at the pay-TV provider.
Michael Vaughan, Mike Hussey, Isa Guha and Mel Jones have also been confirmed as part of a team that already included Brendon Julian and Allan Border.
Gilchrist told Fox Sports on Thursday he is excited to be partnering up with Warne as the faces of a new exclusive cricket channel on Fox Sports.
"Warnie is just superstar material," Gilchrist told Fox Sports.
"Some of my fondest cricket memories were spent in teams with Warnie. Standing next to him was wonderful entertainment.
"The thing that I've admired most about Warnie's commentary is it's just like standing alongside him out on the field or in the change rooms. He is just so honest and you know what he's thinking.
"He's absolutely brilliant at judging cricket tactics and has an astute mind."
