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.
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.
"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."
When it was put to the manager that some of the individual displays bordered on the heroic, Strachan said: "There is heroic in terms of defending. There is also heroic in holding the ball up. Shaun Maloney was doing that, and James McArthur.
"Craig Conway and Steven Naismith went on and did well. I think that's as good as I've seen Alan Hutton play. Steven Whittaker as well. As a partnership at centre-half it wasn't bad too.
"Other ones have to get up to a level of fitness to play at this level and that's hard work."
Speaking earlier on BBC2 Scotland, matchwinner Snodgrass said of the result: "It feels good. We came here believing we could get something. There was loads of pride at stake, the manager gave a few boys a chance and we're delighted with the result."
Croatia had spoken with plenty of confidence ahead of the match, but Snodgrass said Scotland had used that as motivation.
Asked what Strachan had told his players, Snodgrass said: "He just said, 'Everybody can play with heart, run about a lot and do things, but it takes a little bit more now'.
"I think we played a good Croatia side there and got the three points, and I think we could have nicked a few more goals.
"There was loads of cheap talk before the game from Croatia and we used that as motivation to go out there. Every player gave 110 per cent and that's why we got the three points."