The 26-year-old has led his country to a crushing defeat in The Ashes, losing all three Tests so far and prompting criticism from pundit Ponting, who said that Root now needs to "step up big time".
"He's entitled to his opinion but he doesn't spend any time in our dressing room or around the squad," Root told The Guardian. "I'm obviously going to disagree with that. I'm sure if you asked any of the guys in the camp, the coaches or support staff or players, they would back me up on that.
"I don't think I go about things as a 'little boy', for sure. I have my own way of doing things – I think it's important you don't try to be something you're not.
"I know there are occasions where you might have to be quite strong in front of the group. I may not appear to do that out on the field. But there are certainly times when I know that I can do that, and I have done that."
The fourth Test gets underway in Melbourne on Boxing Day.