Brown, 81, the last man to boss Scotland at a World Cup in France 23 years ago, marvelled as the super Scots crushed the Danes at a raucous Hampden Park thanks to goals in each half by John Souttar and Che Adams.
“I would go as far to say it’s the best Scotland performance I’ve seen,” Brown said.
"I thought we were absolutely brilliant. We weren’t playing a Moldova or anything like that, we were playing a top country, ranked 10th in the world.
"Great credit to Steve Clarke because he’s unearthed players when required.
"My worry before it was that we had five top players not available and it might affect the performance, but it didn’t.
"O’Donnell came in there and slotted in brilliantly. He never has a poor game, I think he always does exceptionally well.
"There was an unbelievable atmosphere, the place was buzzing. I was joking with (ex-Scotland player) Roy Aitken and he was joking, saying: ‘When they’ve been to two World Cups, then they can talk’.
"He wasn’t belittling the performance, he was being jocular.”
Monday’s win means the Scots will be among the top six seeded sides in the playoffs so they will be at home for the semi-final tie next March.
If Scotland win that, they go into a final the same month against one of the other five semi-final winners, with a draw to see if it’s a home or away game.
Brown is confident about our chances, such is the depth of quality in the squad.
"We’ve a couple of games to play yet but nobody would worry you playing the way Scotland played,” he said.
"Tierney and Robertson just get better and better and even if Adams hadn’t scored, his all round play was excellent. He holds the ball up, he’s mobile, he’s strong and he's a good finisher.
"In the middle of the park, McGinn, Gilmour and McGregor were outstanding and we have a fantastic goalkeeper and defence.”
The 2022 World Cup finals are in Qatar next November and December.