Joe Root had criticized his bowlers' length after the Adelaide Test defeat.
England on Monday (December 20) suffered a humiliating 275-run defeat in the Adelaide Test against Australia to concede a 2-0 lead in the five-Test series.
Speaking after the game, Root said his bowlers needed to "bowl fuller" and "be a bit braver".
"I nearly fell off my seat when I heard that," Ponting told cricket.com.au. "Whose job is it then to make them change? Why are you captain then?
"If you can't influence your bowlers on what length to bowl, what are you doing on the field?
"Joe Root can come back and say whatever he likes but if you're captain, you've got to be able to sense when your bowlers aren't bowling where you want them to. That's what captaincy is all about."
Ponting pointed out that the only time England bowled full during the second Test was when Root was out of the field due to a groin injury and Ben Stokes was leading the visiting team.
"The interesting thing for me is the only time they bowled full in the game was when Joe Root wasn't on the ground," Ponting said.
"The start of day four when they had a meeting on the ground before play started, Stokes took over the captaincy, and that was the only time in the game they pitched the ball up."
The third Test will be played at the Melbourne Cricket Ground from December 26.