Ponting said his players were entitled to be confident about their chances of winning the five-match series after wrapping up a 277-run victory before lunch today but could not take anything for granted.
''We've started this series very well, from the first day of this Test we've been in total control of the game,'' he told a news conference at the Gabba.
''It's very satisfying to have waited so long for this game to come around and train as hard as we have and keep ourselves prepared for it all to fall into place has been great.
''We'll enjoy this win but it's only one game down.'' Australia also won the first Test in last year's Ashes series in England only to lose 2-1 and Ponting said the painful memory of that defeat would ensure his players would not be taking the English lightly this time.
''We'll just have to have a good look at what we've done well in this game and make sure we continue it in the series,'' said Ponting, who was named man of the match after making 196 and 60 not out.
''You can't afford to take the foot off the accelerator whatsoever.
''It's a good opportunity for us to have a think about the last series and think about the way we might have been thinking going into the second game and make sure we're better off this time around.''
Short Break: Neither team will have much time to reflect on the first Test with the second match starting in Adelaide on Friday but Ponting said the short gap would work in Australia's favour.
''It will be terrific for us, having played as well as we have, there's not much time for England to go away and do too much to get their games in order,'' he said.
''It's always hard work to win a Test match, never matter what the final result is. At different times in this Test match we have been tested as a team and England have probably been under more pressure a lot more than us through this game.''
Ponting also defended his decision not to enforce the follow-on after Australia led by 445 on the first innings, saying it had given his bowlers an extra day to recover between innings while sending England's pacemen back out in the sun when they were showing signs of weariness.
''There were a lot of the reasons behind it and it worked out really well for us. We won the game very comfortably so I'm more than happy with the decision I made,'' he said.
Ponting also scoffed at suggestions England's performance was a result of their short preparation, saying his own team had an even shorter build-up after staying in India for the Champions Trophy final.
''We've only been back in the country for a week and a half before the first Test, so if anyone was going to be undercooked it would have been us,'' Ponting said.
''I don't think they can use that as an excuse. From the moment this game started we got the momentum going our way and they found it hard to get it back in their favour.''