Valeri Kazaishvili's first-half strike condemned Scotland to a repeat of their 2007 result at the same venue in Tbilisi, when a 2-0 win for Georgia all but put paid to Alex McLeish's team's hopes of reaching Euro 2008.
Scotland have slipped to fourth in Group D after they were leapfrogged by the Republic of Ireland, but it could all change again with three games still to play.
Strachan stopped short of describing the visit of Germany to Hampden Park early next as a must-win match.
"I would think we have to pick up something," he told Sky Sports.
“We are still there, so we'll get over the disappointment and we've got to bring that into a good performance."
The result in Tbilisi gave Georgia only their second qualifying win of the campaign, as Scotland struggled to create openings despite the hosts' defence having leaked almost twice as many goals in Group D.
But the Scotland manager felt his side were unfortunate in defeat, suggesting that the players did enough to achieve a better result.
"We did more than enough not to get beaten, but not enough to win the game," Strachan added.
"There was never any real problem with the game. We felt really comfortable, we did what we had to do and made sure there was nothing exciting going on about our box in the first half hour.
"It's vital you don't give away the first goal against a team that's quite used to defending and they were hard to break down. We weren't far away at times but we just didn't have that final touch.
"They tried to pass the ball and to be inventive. They tried as much as they can and that's all you can ask. They gave us what they've got and unfortunately on the night the final pass was short."
Following the visit of Germany, Scotland will conclude their Euro 2016 qualifying campaign with games against Poland and Gibraltar.