Robert Snodgrass grabbed the only goal of the game to clinch a first win of the World Cup qualifying campaign for a side who were rooted to the bottom of the section. The Scots had headed into the clash in Zagreb already out of the race for Brazil in 2014 and favoured by very few to return with any sort of positive result from playing the top seeds.
However, the players delivered a famous win and one that Strachan hopes he can build on for the future, as he said: "It's a great result and we must enjoy the result. But when I look at it from a coach's point of view, there are one or two things you would like to brush up on, that's for sure."
He added: "This is something that makes us happy for a while and makes us feel good about ourselves.
"I think sometimes we do take it badly. I remember James McArthur and Robert Snodgrass taking it badly after the Wales game. Now they can feel good about themselves and hopefully in the next game there is a spring in their step."
Asked if the 1-0 victory has given the nation some pride back, Strachan said at his press conference: "I would think so, I would hope so. You play for your country for pride. It's not for money, it's not for anything else. And you give people pride."
On the result itself, he added: "It's satisfying. The lads played from their hearts. They played as a group, 24 of them trained as a group, which made this possible. So we thank them for that.
"I wanted a performance. It was 90 per cent that we weren't going to win. We would like to think that the work that they put in helped.
"You can't do it if you're not really convinced about doing it and I thought the group themselves were brilliant. We got a response from training and we got a response tonight.
"I really feel pleased for everybody who gets on the plane, who travelled, who were watching. When you're with the national side, the group makes the whole country happy."