The Scots went into the break trailing to a Valeri Kazaishvili goal and could not find a way back in the second half.
Gordon Strachan’s side play world champions Germany at Hampden on Monday night which is where the Celtic skipper quickly turned his focus.
Brown said: “We didn’t get the luck tonight, to be perfectly honest.
“The group is still wide open, there are still nine points to play for.
“We can’t feel sorry for ourselves, we have another big game on Monday night that we have to get ourselves ready for and go to try and get points there.”
Brown added: “We need another good performance. It was an average performance tonight. We know we can do a lot better and hopefully that is on Monday. We had some nice inter-play and a couple of chances and another day that comes off but today it didn’t.
“They shut up shop after they scored their goal. We have bounced back every single game. We have been one-nil down in most games and came back and we have won games from one down. It is all about bouncebackability and we have definitely got that in this changing room.”
Georgia coach Kakhaber Tskhadadze was thrilled by his first competitive victory in the job and took satisfaction from his team’s success in blunting any threat from Scotland for most of the night.
“Scotland did not really have a single, clear cut chance,” said Tskhadadze. “We could maybe have been braver in attack but that will come. Although Scotland were probably the slightly more motivated team, because they have a chance to qualify, it was important for our self-belief to win this game.
“It is teams of Scotland’s level we will be facing in the next World Cup, so it is important for our development that we can compete with teams like them.
“We have a much more difficult game ahead of us against Ireland in Dublin on Monday and we will need to adopt the same attitude there.”
l Scotland Under-21 kick off their latest European qualifying campaign against Northern Ireland in Lurgan this afternoon (kick-off 2pm) under new head coach Ricky Sbragia. The young Scots are in a tough pool which also contains France, Iceland, Macedonia and Ukraine.