"Croatia got a boost from the goal and it was difficult to get the ball off them but, thankfully, we fought our way back into it and there were chances at either end."
Hibs striker Steven Fletcher celebrated his 21st birthday by winning his first Scotland cap.
Playing wide on the left, it was his long pass that sent Miller scampering away for the goal.
He was withdrawn at half-time with an injury but Burley was impressed by Fletcher's contribution.
"He got a whack on the chest, which was a sore one," Burley explained.
"I'd like to have kept him on for longer because he did well. He's got great ability and he's got a great future ahead of him."
Celtic's Stephen McManus, who skippered Scotland for the first time in the absence of Barry Ferguson, was delighted with the display.
"It was great, obviously one of the highlights of my career so far, and I felt the lads deserved a draw if not the win," he told BBC Sport.
And goal-hero Miller added: "Going 1-0 down was a disappointment - it was a really good goal the lad scored.
"But it was good to get the result after going one down.
"We've not had a lot of time to prepare for the game but I think we put what the manager wanted us to do into practice quite well."
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