England sealed an impressive eight-wicket win over the tourists inside three days at Edgbaston on Friday.
It extended a run of alternating between wins and defeats to seven games - the longest such sequence in Tests.
"We are playing very well at the moment but the challenge is to play like that two games in a row," said Bayliss.
England began this series with a 169-run victory at Cardiff, but were hammered by 405 runs in the second Test at Lord's.
The fourth Test in the five-match series starts at Trent Bridge in Nottingham on Thursday and England will win back the Ashes urn with a victory.
"It is good they can put Lord's behind them and put it down to a bad performance," added Bayliss.
"They were disappointed and a little embarrassed in the way they played.
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"To move forward you have to be honest with yourself and admit your mistakes and they certainly were after that game at Lord's. They showed in this match what they are capable of.
"We have a few extra days off now. You get halfway through a series like this and there are always a few little niggles with batters and bowlers, so it will be good to give those an extra couple of days' rest."
England call up Plunkett and Footitt
England head coach Trevor Bayliss has challenged his side to perform consistently after they took a 2-1 lead over Australia in the Ashes.