Scott Brown hit his second winner in two internationals as Scotland stretched their unbeaten run to five games with a third consecutive away win.
Brown lashed home from 18 yards in the 78th minute after Charlie Adam's header had been half-cleared following good work from Steven Naismith and an Ikechi Anya cross.
Strachan wants to see more of such creative play and he was happy to see his side frustrate the hosts for large periods of the game.
"We were a bit fortunate, we understand that, but a lot of things are working," he said.
"We are trying to be more potent when we get the ball back. We need to be more confident and trusting in people, like we did with the goal. We passed the ball and made defenders defend.
"We need more of that but we are getting to understand that. But at the moment people are finding it hard to play against us, which is a start."
Scotland return to Warsaw's National Stadium in October for a European Championship qualifier but Strachan dismissed suggestions the friendly win could have a bearing.
"Absolutely not," he said. "I think we all know that sitting here. It could have gone either way."
Strachan added: "I'm sure there will be more attackers on the pitch for both sides when we play them again. But we saw the stadium and the support and the enthusiasm of the team we will play against."
Strachan, who reintroduced Darren Fletcher to the international fold after a 16-month absence, reserved special praise for Brown, who also hit the winner in Norway in November.
"I thought he was fantastic," Strachan said. "James Morrison was excellent beside him in the first half.
"He's ungamely in a way but he does what all good midfielders do: pass the ball, keep it, move it on. But then he has got the power to win the ball back. He can be really pleased with himself."
Strachan was also delighted with the attitude of 19-year-old Dundee United left-back Andy Robertson, who came on for his debut midway through the second half.
"Andy came on there and the first time he picked it up he drove about 30 yards," the former Celtic boss said.
"I thought: 'that's fantastic'. Absolutely no grey area, I'm going to do what I do. I loved seeing that first touch."