Looking ahead to the fourth Test at Chester-le-Street, starting on Friday, off-spinner Swann said England were always wary of the prospect of Australia finding their groove and had taken no notice of suggestions that the tourists were little threat.
England ensured they would retain the Ashes at Old Trafford when rain arrived at a convenient point during Monday's final day to frustrate Australia, who were on top, and force the draw.
The 2-0 advantage England gained from their wins at Trent Bridge and Lord's means they have achieved their first major objective, but the lead can be reeled in and Australia are aiming to draw the series.
"I'm very confident. Australia played very well at Manchester and they had every right to," Swann said. "I think they had been written off fairly heavily in the media but they hadn't been written off by us.
"So it was no surprise that they bounced back and played well. We didn't have a great game in Manchester so that's something for us to look at and make sure come Friday morning at Chester-le-Street we're back on top of our game."
Swann was speaking in Durham to lend his support to the Sir Bobby's Breakthrough Auction, a charity event looking to raise £1million for the Sir Bobby Robson Foundation, which raises funds for battling cancer in the North East.
The England man is a committee member of the auction and after donating a VIP Test match experience last year, this time he is offering a personal training session.
Speaking at another event which also was raising money for the foundation, former England paceman Steve Harmison expressed surprise at how well Australia's bowlers have performed, and warned they could put the home side in peril again during the fourth Test.
"I thought they would be good but I didn't realise how good they would be and how much homework they've done to put the ball in English areas, rather than the shorter Australian areas," Harmison said.
"If they've done their homework again for this ground they will be a handful and they will be well rewarded."
Harmison, who won the Ashes with England in 2005 and 2009, believes selecting Durham's Graham Onions on his home ground would be a good choice.
Onions, capped nine times at Test level, provides an option if England decide to shuffle their bowling ranks.
Harmison said: "It would be a great shout for Onions to play but I don't think that shout will be loud enough. It's so unfortunate, but who do you leave out.
"I would love to see him play and he deserves his chance and there's no one better than Graham Onions at Durham's Chester-le-Street ground."
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