Charlie Mulgrew's first international goal was enough to seal the tie on a sub-standard Pittodrie pitch, to the delight fo the former midfielder, who amassed 50 caps as a player with Scotland.
Strachan's side resume their World Cup 2014 qualifying campaign with a home tie against Wales next month and the new coach saw plenty of positives to take into that game in Wednesday's win.
| SCOTLAND LATEST
|33/1||Scotland are 33/1 to qualify for World Cup 2014 with William Hill
"I didn't know how I would feel when I first took charge of the team. Now I know. It was an incredible experience.
"I don't think I expected that. I thought I had done nearly everything in the game, played everywhere, and it kind of blew me away really.
"I've been in the Champions League, I have had to beat AC Milan, Barcelona, Man United, and it wasn't like that.
"There were some good individual performances. Everybody knows how the pitch was, it was a problem sometimes.
"You could see the players who have played more regularly and that's got to be a problem for us. The guys who played regularly did a good job.
"Players were picking up good positions but we need to find them earlier. But overall I thought the second half we did really well. It was a horrible day when the surface was bad and they played against a different type of player.
"There was a lot to like and we made chances."