England 3 Scotland 2: Scotland manager Gordon Strachan has replaced defeatism with spirit

Who needs competition when you have this much conviction? This was a friendly match – albeit one much better than we are used to – but Scotland attacked it with a courage, tenacity and purpose that had been desperately missing from the national team for years.

Conviction does not just mean bravery or enthusiasm or pride or any of the basics that every national team can produce. It means a real belief in a plan to win, and it might well be the difference between Craig Levein's Scotland and Gordon Strachan's.

Scotland began both halves with the clear intention of winning, scoring at the start of both. Only two second-half set-piece goals cost them what would have been a thrilling win. A better-directed shot from Steven Whittaker with three minutes left might have earned them a draw.

But the players projected this new feeling and their fans – the loudest at the new Wembley – could sense it. The players that Strachan has are no different from Levein's but they played with a spirit they could barely have mustered under his sorry tenure.

Kenny Miller is not every Scot's choice to lead the line, and might well not have done had Steven Fletcher been fit, but he did not look like a 33-year-old who had flown over from Vancouver for a midweek exhibition game.

Miller was relentless from the start, buying free-kicks from defenders, hassling the corner out of Phil Jagielka that led to the first goal and then scoring the brilliant, confident second, spinning 20 yards out and firing the ball beyond Joe Hart – who could do less about this one than the first – and into the bottom corner.

His partner in relentless annoyance, in endless commitment to the game-plan, was his captain Scott Brown. Experienced players need to lead by example and that is precisely what Strachan had Miller and Brown do. The Celtic midfielder won his running battle with Jack Wilshere, pushing the England man off the ball at will, even darting past him as well.

It would have been too easy for Scotland to sit back and wait, but they pushed England hard when they lost the ball and Brown was at the heart of this, passing and starting attacks with enough precision to frustrate the slow-starting hosts. He even – and Brown does not need much encouragement to do this – played the game with the unapologetic honesty it required, not going out of his way to be friendly with England and letting their players know what he thought of them. Unfortunately for Scotland and Strachan it was not in a winning cause, but there is more than one way to lose a football match and this is far less dispiriting than what they were used to.

Remember the defining moment of Levein's reign, the 1-0 defeat in the Czech Republc in October 2010 when the manager played a 4-6-0 formation, with no intention of winning the game, only to lose it to a set-piece.

Not only did that particular defeat hamper their chances of reaching Euro 2012 – they drew the return fixture at Hampden Park to an unlucky late penalty – but it discoloured the whole Levein era. His was a Scotland team that did not want to win, that hoped to cling on for as long as possible and hope for the best.

Strachan's era might just be different. They have already won one big game under him, beating Croatia 1-0 in Zagreb in June. That was a competitive game in a futile campaign. This was a friendly but one that might just leave hopeful omens for their next long qualification race.