Strachan celebrates "dream" win over Macedonia
Ikechi Anya and Shaun Maloney struck for the Dark Blues in Skopje to lift the nation off the bottom of World Cup Group A.
Strachan's men were presented with a heavily rutted surface at the Philip II Arena but impressed with their slick attacking moves.
Yet the the Scots looked like they would have to settle for a draw after Jovan Kostovski had cancelled out Anya's stunning opener.
But Wigan playmaker Maloney came up with an even more audacious winner as he struck home a 20- yard free-kick two minutes from time to secure the victory.
Strachan told BBC Radio Sccotland: "I'm extremely happy, for the players first of all. To put that work in and play like that and then get hit by a late equaliser was harsh. But we came back again to score and we deserved it.
"I thought they were terrific tonight.
"A draw would have been hard to take. I was coming in on the team bus tonight and I was trying to think how we would manage on a surface like this. How do we win a game of football on this?
"I thought a 1-0 would have been great. But to win it like that was beyond what I would have dreamed."
The 25-year-old gave a glimpse of his talent at Hampden with a couple of pacey runs but his display against the Macedonians was a step up again.
He tormented opposition right-back Daniel Georgievski for much of the first half but proved his quality by slamming under Tome Pacovski on 59 minutes from an almost impossible angle.
But Strachan also hailed the performances of his attacking colleagues Steven Naismith - promoted from an unused sub against Belgium to lead the line as a solo striker - and Maloney.
"Ikechi was good, wasn't he?" said the Scotland boss. "I thought he was terrific. He brought us that wee extra turn of pace, was a threat and made them worry up front.
"But I thought Naismith up front was terrific. Maloney too. We didn't have a failure."
Maloney said after the match that he should be contributing more goals for the side but Strachan felt the player was being harsh on himself.
He said: "Shaun can only contribute more if he gets chances. We didn't have many chances but he plays in a position that is very, very hard. He's a link for us. He can't be too hard on himself."
The victory is just the second of Scotland's World Cup qualifying campaign but lifts the team up to fourth in Group A, with just the final fixture against Croatia at Hampden to come on October 15.
Strachan was happy to see his players smiling once again after the disappointment of defeat against England at Wembley and last week's struggles against the Belgians, but was not keen on an immediate post mortem of the display.
"To walk into the dressing room and see the players all celebrating and hugging each other is what makes management worthwhile," he said.
"We now get on the plane very happy. It's great when that happens after coming back from a performance and a victory.
"But it's far too early for me to analyse anything. Let's just say what a wonderful night, there was some great football, no failures, the fans will have enjoyed themselves and leave it at that. We will analyse it later."