Woakes claimed one wicket for 103 runs in 23.4 first innings over as Australia took command of the Test, with the home side looking to build on their opening win of the series in Brisbane.
Ponting said the inclusion of Woakes over Wood, who played in the first Test, has had a detrimental impact on the influence of England all-rounder Ben Stokes.
“It looked to me as if Stokes was given one job, to run in and bowl bouncers ball after ball,” Ponting told cricket.com.au.
“When he finally got the chance to bowl at a new batsman and pitch the ball, he got a wicket second ball to (Cameron) Green.
“Woakes was ineffective again – I’m not sure why they bothered picking him in Adelaide when they’ve got Wood there.
“To me Wood would have given them a lot more variation in their attack and then Stokes could have pitched it up and bowled like a normal seamer, which he’s good at, and Wood could have taken the role Stokes had.”
Ponting criticised the limited approach taken by England captain Joe Root and his bowling attack.
“Apart from the short-ball plan Stokes executed (on the first day), England didn’t seem to have much of a plan after that,” Ponting said.
“It was run in and bowl back-of-a-length and wait for the Aussies to make mistakes.
“Well, when you’re bowling to two of the top three batsmen in the world, they’re not going to make mistakes. You’ve got to find a way to get them out and change things up.”
Australia reached 473-9 before declaring in the first innings while England were 17-2 in reply at the end of the second day’s play.