Brown was the last man to lead the Scots to a summer finals when his squad qualified for the 1998 World Cup in France.
A year later Scotland suffered anguish as they lost out in a two-legged play-off against England that denied them a place at Euro 2000.
England triumphed 2-0 at Hampden before Don Hutchison’s header gave Scotland a consolation 1-0 win at Wembley.
Brown admits he is “desperate” to see Scotland win against England at Wembley in Wednesday night’s friendly but insists that it is far more important for Gordon Strachan’s team to make Euro 2016 in France.
“Gordon is already a legend in Scottish football and a win would help that,” Brown said. “But he doesn’t need to beat England to cement his legacy.
“I think it’s more important that we qualify for the European Championships next time than it is to win at Wembley.
“But a win against the Auld Enemy would be a bonus.”
Strachan took over as Scotland boss following a disastrous start to World Cup qualifying and a recent 1-0 win over Croatia in Zagreb has raised hopes that the side may have finally turned the corner.
And Brown is in no doubt that Strachan will field a side capable of upsetting England, whose players may have one eye on the start of the Premier League season, which begins this weekend.
“I never felt pressure at any time during my time as manager of Scotland and neither should Gordon,” he said. “I always worked to the philosophy that if you do your utmost, then that was all you could do.
“I was fiercely determined and competitive but I didn’t lose any sleep. People asked me after we lost here 2-0 to the English in 1999 if I feared we were going to be humiliated in London. But I never felt that way. I was always optimistic because I had faith in my team.
“I still feel the same with this group and as a fan I’m optimistic. I’m desperate for us to win the game on Wednesday.
“It will be very tight. In the last 10 games against England neither side has scored more than two goals. It will be a mistake, a poor decision or maybe a penalty that decides it.
“The only piece of brilliance I can remember in this game was Paul Gascoigne’s goal at Euro 96. But I don’t think you will see that this time. I think it will be dour. There will be one goal in it.”