But the midfielder revealed it was the manner of the triumph achieved against Estonia – thanks to a first-half goal from Charlie Mulgrew – and the quality of players available to come on which pleased him most.
That's what gives Brown hope that, when the World Cup qualifiers resume next month with must-win matches against Wales and Serbia, the feel-food factor will be there to back up the nation's push to get back into the race for Rio.
The skipper was one of six players replaced during the win at Pittodrie and said: "It showed you the quality we have when the manager took players off and he was able to replace us easily. We have got strength in depth in this squad, and that is one of the most reassuring things for us to see someone coming on and it is not weakening the team.
"All the lads are turning up for the games, and that shows how good the spirit is."
Strachan will try to further build this in the weeks between now and announcing the squad for the matches against Wales and Serbia next month.
Brown – who reported he has no fitness issues after playing an hour on a difficult surface – believes they can now look forward to these games with fresh hope and belief after last night's showing.
He said: "The manager told us in the dressing room after the game last night that he was happy with us and pleased that we won.
"It is going to be good to have 10 days with the manager for the double header next month.
"He will have a lot of input, and be able to set up a lot of formations and set plays.
"We can't talk too much about that at the moment. But I'd like to think and hope that there is momentum building after the wins over Luxembroug and now Estonia.
"Performance is always important, and we were pleased with that last night. But we are a team that always wants to win games.
"We don't just back off teams, and I think that showed last night, especially in the first half when we were pressing high up the park and putting Estonia under pressure.
"It's what the manager asked us to do, and it's good to play in that formation.
"It's more attacking than what we have been used to.
"You then have guys like Shaun Maloney pushing high up the park and getting into one-on-ones with opponents.
"His feet are so sharp and he takes chances, which is great to see."
Goal-hero Mulgrew added: "It was difficult conditions however the most important thing for us was to get the win so we are happy.
"It is good to get that winning spirit – hopefully we can go on and get more wins."
Chris Burke, who made his first Scotland appearance since 2006, said: "It's been excellent, him (Strachan) and his coaching staff, I've learned so much so it's great to be amongst it all."
"It was excellent, I was happy with my performance – all round the team did well."