Back-up seamer Andy Bichel will lead the world champions' pace attack because of injuries to Glenn McGrath, Jason Gillespie and Brett Lee.
The inexperienced Nathan Bracken and Brad Williams and recalled Queenslander Michael Kasprowicz will assist Bichel in the tournament which also involves New Zealand.
"We've got our backs to the wall a little bit with our injuries and preparations, but we won't be using those as excuses," Ponting told reporters at Sydney airport.
"Going to the World Cup as favourites and defending champions, we were under a fair bit of pressure there as well.
"But I think the side is going to be tested more this time, with the injuries we've got, to key places to key bowlers especially. It's a big test for us."
Leg spinner Shane Warne's understudy Stuart MacGill will also miss the series with a calf muscle injury. Warne's 12-month doping ban ends in February.
New South Wales batsman Michael Clarke, 22, has replaced injured left-hander Darren Lehmann, who is acknowledged as one of Australia's better players on turning wickets.
"Both sides that we're playing against are very good one-day sides and they've been playing in those conditions for the last few weeks," said Ponting, 28, who has a record of 37 wins from 47 matches as captain since succeeding Steve Waugh last year.
Australia, who completed a 2-0 Test series win over Zimbabwe this week, will play India on Sunday.
New Zealand begin the tournament against the hosts on Thursday. The final is on November 18.
India's Sachin Tendulkar, one-day cricket's leading runscorer, averages 58.45 in 11 matches against Australia on home soil.
"His record against Australia would be fairly outstanding so that is a bit of a worry, but we'll keep our fingers crossed that we can hopefully get him out early," Ponting said.
