Ahead of Australia's opening World Cup match against Scotland in St. Kitts on Wednesday, Gavaskar said there was a lack of warmth towards the Aussies over what he called their "awful" behaviour.
But Ponting said his team's behaviour had been "reasonable" in recent times.
"I have probably been reported more than anybody since I became captain," Ponting told Monday's Daily Telegraph newspaper.
"It's something we pay a lot of attention to. I don't mind if 'Mr Perfect' (Gavaskar) comes out and goes on about our team, I know we are all not perfect.
"We are not going to keep everyone happy 100 percent of the time. But for some of these guys that have done it all themselves, it's pretty high and mighty for them to say that."
Australian players were reported seven times last year for breaching the ICC's code of conduct, with Ponting and fast bowler Brett Lee found guilty twice.
In his comments in the respected India Today magazine, Gavaskar said many people were happy at Australia's defeats to England and New Zealand in recent one-day series.
"Australia's come-uppance at the hands of England and New Zealand has gladdened the hearts of not just the other aspirants for the World Cup but also the followers of the game," he wrote.
"There is not the slightest doubt that in the last decade or so the Aussies have been awesome in batting, bowling and fielding which has taken them to the top of the cricketing ladder in both Test and limited overs cricket.
"But they have also been awful in the way they have sometimes behaved on the field much to the chagrin of the traditional fans of the game.
"Unlike the West Indian teams of the 1970s and 1980s which dominated world cricket in much the same way as the Australians are doing now, the Australians are not popular."
Ponting, however, retorted that India should look at their own record.
"I don't know if there are too many popular winners," he told the Daily Telegraph.
"If you are really dominating teams for a long period of time, I don't think you end up having too many supporters around the place.
"We all know the way he played his cricket, don't we? If he is talking about us, what about the way India have played their cricket over the last few years."
He noted India's miserable Test record in 2006 where they won just three of 12 matches, while the Australians enjoyed an unbeaten run.
"I know who I would rather be going to watch. Have a look at how many Test matches they have won," Ponting said.
"He (Gavaskar) has been a big part of that, he has been a selector and he has been on the coaching committee.
"They might want to start to look at the way they play their own cricket rather than looking at us."