Despite the scoreline suggesting otherwise, Brown believes that Scotland's performance was symbolic of their recent resurgence under Gordon Strachan.
"We're getting the belief back. We're looking strong and we got the three points, which is the main thing," he is quoted as saying by Sky Sports News.
"We have got to take every positive we can from it. We created chances and could have been three up at half-time. We defended really well and were solid all the way through. They didn't even have a shot on target, so it tells you how well we defended."
Scotland continue their qualifying campaign on Tuesday when they face Poland in Warsaw.