Michael Vaughan thought England's chance of victory had gone when Australia needed just three runs to clinch an amazing win.
Vaughan said: "It's been an epic game. I think most of my guys thought it had gone but we fought hard.
"We were 1-0 down and you can't afford to go 2-0 down against Australia. We've won and it sets up the series.
"I firmly felt if we had lost the game, gone 2-0 down, I don't think we'd have come back from that."
Australia needed 107 runs to win at the start of the fourth day with just two wickets remaining.
But they refused to give up hope, with Shane Warne, Brett Lee and Michael Kasprowicz combining to add 104 for the last two wickets.
Warne hit a defiant 42 before treading on his wicket and Lee ended the game unbeaten on 43.
Vaughan added: "I really thought a hundred runs on the last morning was going to be too much but Shane Warne's had an outstanding game and so has Brett Lee.
"But my team came out at the end and showed great character."
Steve Harmison, who took the final wicket to clinch victory, praised Vaughan's ice-cool nerves and tactical nous.
"I think everybody in an England shirt was probably panicking but we held our nerve and managed to scrape home.
"Vaughany's been great throughout. Fred (Flintoff) got a lot of praise but Vaughany was awesome," he said.
"Some of his decisions were excellent - bowling changes, fielding positions. And right down to the last minute he was calm and just said, 'Get 'em out."
Wicket-keeper Geraint Jones expressed relief after taking the catch off Mike Kasprowicz to complete the win.
"One of the main things I had in my mind was if the ball came my way I was going to catch it," said Jones, who missed two chances in the first Test.
"It was an incredible morning and to finally get one off Kasper's glove down the leg side was a great relief.
"It was probably the most important catch I've taken so far."