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."