The midfielder was handed the armband by new boss Gordon Strachan for the friendly at Pittodrie in the absence of Darren Fletcher.
As Celtic skipper, Brown is used to shouldering extra responsibility and would jump at the chance to take on the role again for the national team.
He said: "It was amazing. It was a great honour and I would love to do it again.
"I've got a lot of responsibility at Celtic and there are a lot of great lads here as well to help me out and it's just been phenomenal."
Brown has been troubled with an ongoing hip problem this season and was pleased to be able to contribute to Strachan's first match in charge for an hour of the game.
He added: "I'm not too bad. It was a good run out and I got 60 minutes under my belt. I think the lads played really well."
Hoops team-mate Charlie Mulgrew grabbed the only goal of the game to open his international account and allow the Strachan era to begin on a positive note.
Brown said: "There are a lot of things we need to work on but we are slowly getting there.
"We've got a new manager in, all the lads are very keen and we've been enjoying training.
"We need to try to improve on results and improve on our home performances as well and just take it from there."
The Scots were in need of a morale-boosting result following a dismal start to their World Cup qualifying campaign, which ultimately cost Craig Levein his job.
And, although far from spectacular, the outing on a poor playing surface at Pittodrie provided enough cause for optimism under the new regime.
Asked if the result or performance was most important on the night, Brown said: "It's a bit of both.
"We performed quite well and we kept a clean-sheet as well, which is a good thing, and we came away with a win.
"I think we pressed them a little higher up the field.
"It was more or less the same formation but we just pressed them higher and put the centre-halves under a little bit more pressure.
"The conditions weren't the best but it was the same for both teams really and I've played on a lot worse."