Scotland were beaten by Wales for the second time in Group A and the national team sit bottom of the table after failing to win in five games.
The Wales defeat marked Gordon Strachan's first competitive match as coach but winger Burke is confident there is a bright future ahead for Scotland.
"There is nothing but encouragement and positives," said Burke. "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."
Scotland had taken the lead through Grant Hanley, but the match turned when Robert Snodgrass was sent off after conceding a penalty, which Aaron Ramsey converted before Hal Robson-Kanu headed Wales' winner.
Burke added: "Wales came out the traps very well, played some very, very good stuff and kept the ball a lot. We had to be patient and weather the storm.
"In the end we were 1-0 up at half-time and I thought we started very well in the second half. It's about taking your chances and making them count when you're on top, especially at international level.
"We were very positive and we were looking good and looking for that second goal.
"Snodgrass hit the post and there was a little chance for myself when my shot was blocked, I should maybe have done a bit better. And the sending-off and the penalty was the turning point."