Second-half goals from Ikechi Anya and Shaun Maloney delivered a 2-1 win in Skopje which lifted Scotland off the foot of Group A.
The result and a generally lively performance also maintained the sense of momentum which had been in danger of petering out after the June win in Croatia was followed by defeats by England and Belgium. When asked if the pressure had been building on him, Strachan broadened his answer to include the whole team: "I would imagine most of the players would think that there was pressure, whether it was an individual thinking 'I must prove myself', or as a group. To come away with a performance like that is terrific. It's another part of the jigsaw. We're not a great side by any manner of means but we can do terrific things at times.
"As I came to the game I couldn't imagine it being played like that, I thought it would be far scrappier with scrappy goals but it didn't work out that way.
"We weren't allowed to train on the pitch last night. We were only allowed to train on half a pitch so we thought, well, the other half can't be very good either. The UEFA observer said the pitch wasn't good enough to play on. There were a lot of divots put in and sand put on it. The Macedonians tried their best. So to play football like that on a surface like that was a huge bonus.
"What was the most pleasing thing? Everything really. When you drive to the game you look at the surface and you think a win would be great. You wonder how you might win. A couple of breakaways, you try your best. But to play like that and to get the win . . . that was terrific, and against a side who beat Wales.
"In the first half we were exceptional, in the second half we were good. We expected Macedonia to come back at us, we expected the manager to say things at half-time and they did that. But, we still tried to play. At all times we tried to play."
Anya's performance, on his first start for Scotland, was one of the night's real highlights. "He must
be pleased with himself," said Strachan. "And he could only give the right-back a torrid time because the rest of the players were brave on the ball to build it up and give Anya the chance to be one-on-one. There had to be a lot of passes and be brave before he was on the ball. You don't just give him the ball and hope for the best. You have to build up the play, suck in their back four and then give it to him."
Strachan also praised Maloney's dedication and professionalism, which he said was shown by his cool free-kick for the winner three minutes from time. "Good players can deal with pressure and can take free-kicks and corners at the right time. That's not a fluke.
He's been practising since I first knew him eight years ago."
The match had a bizarre moment in which French referee Fredy Fautrel started the second half only to blow his whistle and stop play seconds later when he realised Macedonia goalkeeper Tome Pachovski was late coming out of the tunnel.
"Brilliant! And he blew his whistle," added Strachan. "There was no reason for him to blow his whistle. It was one of those things we will talk about for a long time. He should have played on.
"He cannot stop the game at any time until the ball goes out of play, and then he gets on. That is my understanding of the rule.
But who cares . . . we won!"