Niall McGinn's stunning early strike was enough for the Dons as they were rarely troubled by Kilmarnock but were also unable to put the game to bed despite a number of chances - especially after the introduction of Josh Magennis midway through the second half.
Shiels said: "I thought we played well in the first half. We sustained our belief in how we play and we made a few mistakes but we looked the most fluent of the two sides.
"Conceding the early goal didn't help and there were a lot of stoppages for free-kicks. We chased the game, and I thought we showed great promise.
"In the second half, we seemed to drop a little bit deeper and give them more territory. Every single chance they had, bar one, was the result of mistakes from young players learning the game."
Since the split, Kilmarnock have now lost consecutive games without scoring a goal, but Shiels felt that his side showed confidence is not a factor in those results.
"If you were summing up the performance, you would say it was a brave performance," he said. "They were brave in where they took the ball, and they were brave in the position they got into. It's not as if we're lacking confidence."
Shiels highlighted the goal as the difference between the two sides, continuing: "That's why Niall McGinn is one of the nominees for (SPFA) Player of the Year. He deserves it and he scored a fantastic goal."