But with the third Test starting at Old Trafford on Thursday, Vaughan said it was vital England made the most of their recovery from last month’s 239-run first Test defeat at Lord’s.
"I asked the boys before this game ‘Could we show some character and bounce back from Lord’s?’ It is fantastic that we have done that and now we have to try for something similar in Manchester," Vaughan said after England won with more than a day to spare.
"The most important thing now is to take this momentum into the third Test and start well again on Thursday at Old Trafford," Vaughan added after Sunday’s thrilling fourth-day climax.
"I don’t think we would have come back from 2-0 down against a team like this," Vaughan, looking to become the first England captain in nine series and 18 years to win the Ashes, admitted.
England all-rounder Andrew Flintoff assured himself of a hero’s welcome at his Lancashire home ground after his man-of-the-match display at Edgbaston.
The 27-year-old fast bowler and hard-hitting batsman took seven for 31 and made vital scores of 68 and 73, the latter innings particularly crucial as he shared a pivotal last-wicket stand of 51 with Simon Jones.
"He didn’t score a 100 or get five wickets in an innings but the two scores he made really gave us momentum and the stand with Simon Jones was the real momentum swing in the game.
"We could have been looking at around 230 to defend. To get it up to 282 swayed the momentum back into our favour and Freddie gives us a real belief to go out there and bowl and get some wickets.
"His spell on Saturday night was fantastic when he got two wickets in that first over. There were so many twists and turns in the game but both the last wicket partnership and the first over that he bowled were real turning points."
Even so Australia, finishing on 279 chasing 282, almost got home after resuming Sunday on 175 for eight needing a further 107 for victory.
Brett Lee was left on 43 not out when last man Michael Kasprowicz, on 20, gloved a catch down the leg side through to Australia-raised keeper Geraint Jones off fast bowler Stephen Harmison.
"Towards the end they were playing nicely and it was looking as if we weren’t going to get over the line," Vaughan conceded.
But he insisted he hadn’t given up hope even when Simon Jones dropped Kasprowicz at third man with Australia still needing 15 to win.
"I always felt there would be another opportunity and we would be good enough to take it. We held our nerve and it was a fitting end to a great game of cricket."
Australia captain Ricky Ponting, who played in the team that tied the 1999 World Cup semi-final against South Africa at Edgbaston, said: "That is the most nerve-wracking end to a Test I have played in.
"We had a great win against Pakistan a few years ago in Hobart when Adam Gilchrist got us home when we were out of the game completely.
"This game is right up there with any game of cricket I’ve played in and that includes tied World Cup semi-finals and all that sort of stuff.
"We’ve got very close to pulling off an unbelievable win and we haven’t quite got there but I actually feel quite happy at the moment.
"I was disappointed when you see the ball ballooning off the glove down the leg side and the game is taken away from you but we can take a lot out of this game, especially what has happened over the last two days.
"Hopefully that can spur us on to playing some better cricket in the third Test when we will look for our top order batsmen to score more runs."
Flintoff, playing in just his second Ashes Test after managing a mere three runs at Lord’s, said: "A lot’s been written about this Test match, words like ‘extraordinary’ and ‘unbelievable’ and it lived up to that at the end.
"Brett Lee played fantastically well. He stuck in and had answers for everything we threw at him.
"I just congratulated him on a great effort, it was something to be proud of. His back was against the wall but he came out fighting. It was an unbelievable effort."