Ponting had questioned Pakistani umpire Asad Rauf's call for a wide in the 33rd over of the West Indies innings, which led to Aussie skipper being fined his entire match fee.
''Let's be clear, Cricket Australia doesn't condone any actions that go outside the Spirit of Cricket. We've worked very hard with Ricky and our players to ensure it is observed at all times,'' CA acting chief executive Michael Brown told The Age newspaper.
''It's a concern for Ricky and it's a concern for us. But the fact he's taken the initiative to publicly and privately address these issues will ensure he and his team go forward from here. We've got to be positive in that regard,'' he added.
Brown said Ponting spoke to him after the match and made it clear to the captain that any such behaviour was unacceptable.
He said Ponting should learn from experience and refrain from such conduct as he risks possible suspension for any further outbursts now or in the Ashes later this year.
This was Ponting's second such offence in the last 12 months -- the other took place during the second Test in Bangladesh in April -- and it was why the charge was upgraded to a level two offence.
Ponting was also fined during the fourth Ashes Test last year for an outburst directed at the England dressing room after he was run out by the substitute fielder Gary Pratt.
The level-two offence can carry a suspension of two ODIs or one Test, and the match referee is entitled to consider the player's previous history.