Cricket Australia is reviewing whether issues like ball tampering and sledging have been part of country's cricketing culture but the straight-talking Ponting refused such perception.
The players were sent home from the tour after the third Test and apologised for their actions.
"I have today let Cricket Australia know that I fully accept the sanctions imposed on me", Warner said in a tweet posted Thursday.
Ricky Ponting said Australian cricket was moving in the right direction with the fallen trio of Steve Smith, David Warner and Cameron Bancroft accepting sanctions imposed by Cricket Australia and the uproar surrounding the ball-tampering scandal in South Africa finally dying down.
The fallout from the saga has been significant with Steve Smith and David Warner being stripped of the captaincy and vice captaincy as well as handed one-year bans.
"Our task is now to work through this problem and make sure cricket (in Australia) comes through it much more strongly".
Warner admitted last week that he was resigned to not playing for Australia again.
Warner, who was identified as the ring leader of the plot to doctor the ball during the third Test in Cape Town - will now sit out cricket in Australia until March 2019. Cricket therefore needs to take decisive action to restore its rightful position in the hearts and minds of all Australians, that's why we need a far-reaching and comprehensive review of the culture of the game.
Smith held a teary news conference hours later in Sydney, where he took the blame for the episode happening on "on my watch" and asked for forgiveness.
But the players will continue to be paid their CA retainers‚ in Smith's case the equivalent of R17.9 million a year and Warner R12.6 million. In fact, he felt the players have already copped a bigger punishment than what should have been given if one went by the rule book.
The three erring cricketers were earlier given time till April 11 to decide whether to appeal against the Cricket Australia penalties or not. "It has also been humbling to be reminded of the passion all Australians have for our great game".
"We, as Australians, like to play our game hard, we like to play our game fair and our fans expect us to play that way".
Dyer said the ACA were providing ample support to the the players who were now "doing it tough and beginning a hard time in their lives", and assured cricket-loving fans that they would endeavour to learn from their "errors of judgement".
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