Scott Brown's superb finish from 18 yards ensured Scotland stretched their unbeaten run to five games with a third straight away win and Strachan was pleased with what he saw in Warsaw.
"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.
"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."
Scotland return to Warsaw's National Stadium in October for a Euro 2016 qualifier and Strachan reserved praise for Brown following his winner.
"I thought he was fantastic. James Morrison was excellent beside him in the first half," he said.
"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."