The 27-year-old midfielder led Strachan's side for Wednesday's friendly at Pittodrie in the absence of regular skipper Darren Fletcher.
And the Celtic captain says he would be delighted to shoulder the responsibility again for the national side.
"It was amazing. It was a great honour and I would love to do it again," admitted Brown. "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."
Charlie Mulgrew scored the only goal of the game to get Strachan's reign off to a positive start and Brown believes the former Coventry, Southampton, Celtic and Middlesbrough boss is gradually starting to mould the team to his liking.
"There are a lot of things we need to work on but we are slowly getting there," added Brown. "We've got a new manager in, all the lads are very keen and we've been enjoying training.
"We performed quite well and we kept a clean sheet as well, which is a good thing, and we came away with a win.
"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.
"We need to try to improve on results and improve on our home performances as well and just take it from there."
Scotland's next fixtures see them return to 2014 World Cup qualifying action as they host Wales on 22 March before travelling to Serbia four days later.
Strachan's side currently sit bottom of Group A with just two points from four matches.
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