England, set a huge target of 383 to win at Old Trafford, were bowled out for 197 following some spirited lower-order defiance.

Victory left Australia 2-1 up in the five-Test series ahead of next week's finale at the Oval.

"I'm bitterly disappointed," England captain Root told BBC Radio. "I thought the way we fought today, the character we showed, every single one of them can be proud of that today.

"To come so close to taking it to the Oval is hard to take. We've still got to look forward and make sure we level the series.

"I think it's been a good Test wicket, an important toss to win, and we were not quite at our best in the first innings. We fought hard and bravely throughout the game, but we're in the position we are now."

Root hailed Steve Smith, who has scored an astonishing 671 runs at 134.2 including three hundreds in the series despite missing England's one-wicket win in the third Test at Headingley with concussion.

"Steve Smith has played very well," he said. "He's a world-class player. You need to take any chance you get at him early. The first Test is probably the difference between the two sides.

"They've bowled well. I think the way we went about our business today was impressive. The guys will take a lot from that.

"You learn a lot about your team and players in situations like this and we stood up to the challenge and fought bravely."