Scotland started the better side in Tbilisi but struggled to carve clear chances. The hosts improved and Valeri Kazaishvili fired them in front in the 37th minute after no blue-shirted player could close him down quickly enough as he brought down a headed knockback 18 yards out.
Shaun Maloney nearly scored direct from a corner and Steven Fletcher hit the post but a foul on the goalkeeper was given the first time and the offside flag went up the second time.
Scotland failed to test the home goalkeeper and a succession of crosses and corners came to nothing in the final 15 minutes.
Strachan said: “We didn’t do enough to win the game. We definitely didn’t do that much wrong to lose the game.
“The game looked like a draw but if you get the first goal, life is a lot simpler. We had to play catch-up when we lost the goal.
“Before that, apart from one break, I didn’t see any problems in the game. I felt comfortable. I was looking to get to half-time and tell them to up the tempo and think about a couple of things.
“Then they scored and put on a great defensive show and got behind the ball and ready to break. Even then I didn’t think there was a problem for us. I thought we were a couple of yards away with our passes and intricate moves to try and get through, because we don’t have the physical presence to fight them for a goal.
“The lads were brave on the ball but maybe just a wee bit now and then, a foot or two here and there, we couldn’t get through and it wasn’t to be.”
Nukri Revishvili’s only save came from a deflected Charlie Mulgrew cross but Strachan said: “We can’t just throw balls in there, we are not big enough or strong enough. So you have to work our way in there. If you want to do that you have to be precise. That was missing.
“You only need one of those balls at somebody’s feet and you’ve got a chance.”
Georgia manager Kakhaber Tskhadadze, who replaced Temuri Ketsbaia midway through the campaign, felt his side’s second win in Group D was a major step forward but warned they have a tougher task in Dublin on Monday.
Tskhadadze said: “I’d like to thank everyone for their support and especially the fans. It was a pity there were not more people here but hopefully the crowds come back.
“It was important for our self-belief to win because it’s teams of Scotland’s quality that will be competing for places in major finals.
“The team were fantastic, especially the defence. Scotland did not really have a clear-cut chance.
“It’s no reason to celebrate for long though because we have a more difficult game in three days’ time against Ireland and we will be focused on that game in a few hours.”
Revishvili, Lobjanidze, Kvirkvelia, Amisulashvili, Navalovski, Okriashvili (Merebashvilli 71), Ananidze (Daushvili 82), Kashia, Kankava, Kazaishvili, Mchedlidze (Vatsadze 90).
Marshall, Hutton, Russell Martin, Mulgrew, Robertson (Hanley 59), Anya (Griffiths 75), Brown, Maloney, Morrison, Naismith (Forrest 59), Steven Fletcher.
Ovidiu Alin Hategan (Romania).