There had been suggestions Arthur paid the price for disciplinary issues haunting the team, which included vice-captain Shane Watson, Mitchell Johnson, James Pattinson and Usman Khawaja being punished for failing to make a presentation on how the team could improve, an incident which became known as 'homework-gate'.
Opening batsman David Warner was also suspended from the team earlier this month after attacking England batsman Joe Root in a Birmingham bar. But Ponting said in his Daily Mail column: "The off-field problems in India, and the latest with David Warner, may not have helped, but the simple fact is results haven't been good enough. If you win, a lot of the stuff focusing on peripheral matters disappears."
He added: "When I heard the news about Mickey I turned on the TV and the stats from his time in charge flashed up on the screen. It is the number of Test and ODI victories on his record that are relevant, not the way he dealt with Warner. Frankly, I'm not sure what more he could have done to avoid that particular incident with Joe Root happening anyway."
Ponting was full of praise for Darren Lehmann, Arthur's successor, who he believes can raise team morale ahead of the Ashes series which gets under way at Trent Bridge on July 10.
Yet the 38-year-old stopped short of hailing the decision to appoint Lehmann as one that could give Australia the edge against England.
"'Boof' has had a lot of success as a coach and even though I have never played under him I know exactly what he'll be like around the Australia team. He will bring calmness to the group, make sure they try to have fun and enjoy the experience of playing for Australia," added Ponting.
"Above all, he will instil confidence into the young guys in the team who seem to be lacking it at the moment.
"Will this decision affect the outcome of the Ashes? Well, only time will tell. Australia could have won the first Test under Mickey Arthur and equally they could win it under Darren Lehmann. What I do know is that they need to be aggressive and take England on now. They will under Boof."