Australia called up two more quick bowlers to their squad for the second Ashes Test as they continue to search for the killer touch that again eluded them in the first Test at the Gabba on Monday.
The once-dominant Australians have got into the habit of letting teams off the leash from strong positions recently, most notably in a Test defeat to India in Mohali last month.
Australia were again in charge with a first innings lead of 221 on day three of the Gabba test but England batted for two days to earn a morale-boosting draw.
"We got ourselves in a good position in the game through our batting," said Ponting.
"Even this morning coming to the ground I felt only one team was good enough to win this game if we were good enough to take some early wickets.
"We weren't good enough this morning so it ended up unusually being a drawn game at the Gabba," he added.
Australia responded by calling up Ryan Harris and Doug Bollinger to supplement their fast bowling corps of Mitchell Johnson, Peter Siddle and Ben Hilfenhaus for the Adelaide test, which begins on Friday.
"We have to work to work out what is the best attack to take us 20 wickets in Adelaide," Ponting said.
"No doubt that we've got a lot of improvement to do with our bowling group.
"We didn't bowl as well as we could by any stretch of the imagination ... I felt like I exhausted every option as far as fielders and tactics, we just weren't able to break their top three or four players.
"If we get a flat wicket in Adelaide again, we've got to make sure we're a whole lot better than we were in this game," he added.
Bollinger, who is returning from a side strain, was left out of the team for the first test in favour of Siddle, who took a hat-trick and six wickets in England's first innings.
Harris, who is also on the comeback trail after knee surgery, was included in the original 17-man Australia squad for the first test.
"He's had some niggly knee problems," said Ponting.
"I understand at the moment that he's going particularly well in the (Sheffield) Shield match he's playing at the moment and everybody I've spoken to said that injury he had will be fine for a Test match," he added.
Johnson had a particularly poor test, going without a wicket at the cost of 170 runs. "I have seen him bowl better," Ponting said.
"But I wouldn't want to single anyone out because I don't think any of our bowlers were at their best in this game," he added.
Australia squad: Simon Katich, Shane Watson, Ricky Ponting (captain), Michael Clarke, Mike Hussey, Marcus North, Brad Haddin, Mitchell Johnson, Ben Hilfenhaus, Peter Siddle, Doug Bollinger, Ryan Harris, Xavier Doherty.