Goals from Aaron Ramsey and Hal Robson-Kanu within 90 seconds gave Wales another 2-1 victory after Robert Snodgrass had received a second yellow card following a needless and late penalty-box challenge on Chris Gunter to hand the Arsenal midfielder the chance to level from the spot in the 73rd minute.
Snodgrass had earlier hit the post with a curling effort as Scotland built on Grant Hanley's headed opener in first-half injury-time, and Burke said: "There is nothing but encouragement and positives."
He went on: "Obviously things will take time, when a new manager comes in it doesn't happen overnight. But we have been very impressed with what the manager and the coaching staff have brought in. He wants us to play football and I think we showed that in patches. We will be looking to do that more often."
New boss Gordon Strachan, whose plans were disrupted when Steven Fletcher had to be replaced by Kenny Miller after injuring his ankle in the second minute, promised changes for the trip to Serbia in midweek.
He said: "It is not an easy period for us. We need to try to win games. We will experiment and find out what is right for us and take it from there. It is an opportunity for other people to stake their claim
"The game changed on the penalty. At 1-0, it flattered us but you have to score the second and we had chances to do that but we never took them.
"Steven Fletcher's injury spooked us a bit.
"The penalty causes us a problem, they score right away after that and it is uphill fight after that."
On Fletcher's ankle injury, Strachan said: "His ankle buckled. Fletcher was a bit shocked but he is more relaxed now. He is getting assessed and he will get assessed by his club."
- Sports & Recreation
- Steven Fletcher
- Robert Snodgrass