Ponting said his team was determined to uphold the spirit of cricket and learn from their past mistakes.

"I have been surprised by the reaction of some in the broader community who believe we did not play that amazing Sydney Test in the spirit of the game.

"We take the spirit of cricket very seriously and are determined to ensure we are not only remembered as a good team but one that is respected throughout the cricket world for the way we play," he wrote in a column in The Australian.

The Aussies held a team meeting on Sunday to discuss the events during and after the Sydney Test.

"That is why I led a meeting this afternoon of our team and other cricket officials, where we revisited our spirit of cricket pledge," Ponting wrote.

He said the team has discussed the areas of improvement and would be careful in those issues.

"We looked back at last week's game and discussed little areas where we believed we could improve things. No one is beyond criticism or bigger than the game.

"Life's all about learning little things day by day, and it's no different playing in a successful cricket team. You always find little ways of improving yourself," he said. Ponting admitted he and Michael Clarke should have behaved better during the controversial Sydney Test.

"I know when I was given out in the first innings in Sydney, I should have left straight away instead of hanging around for a few seconds, and I know I should not have lobbed my bat into the dressing room.

"Michael Clarke also knows that he should have gone straight away too, after cutting the ball to first slip. He knows he did the wrong thing, but at the time he was just shocked at how he had got out first ball," he said.

The Aussie skipper, however, said his team did not commit any grave mistakes in the second Test.

"I believe there are no glaring issues we need to address, but when they are all added together in the heat of such a tense and dramatic final day, they caused a reaction, so we need to tighten up on how we play.

"We are very keen to ensure we get the balance of how we play the game right so we can focus clearly on another very big match coming up, this time the third Test in Perth, with the possibility of a record 17th consecutive win if we're good enough in this game," the Australian captain wrote.

Ponting said the sharp media reaction after the Sydney Test had disturbed him and his family but the support of Cricket Australia had a calming effect.

"The day after the Sydney Test, I got up early and went to play golf. I had played four or five holes when I took the phone out of my bag and checked for messages. I had a missed call from my wife, Rianna, so I rang her back and she was concerned that one of the newspapers had called for my sacking as captain," he recalled.

"I rang Cricket Australia Chief Executive James Sutherland straight away and got him to read parts of the story to me.

"At the same time he said: 'Look, let's get this all into context. You've got 100 per cent of my support and I know you've got 100 per cent of the Board's support.'

"I rang Rianna back and reassured her that everything was okay."

Ponting also appreciated his teammates for handling the volatile situation in the right manner.