The Eagles missed the chance to climb out of the bottom three of the npower Championship after James Vaughan, Pablo Counago and Neil Danns all squandered good opportunities to score.
Vaughan, on the final appearance of his loan spell from Everton, should have broken the deadlock just before half-time but scuffed his shot wide.
Counago and Danns were also denied by some last-ditch Hull defending as the visitors held out.
"You could say maybe we were unfortunate," said Burley. "There were three or four point-blank blocks when the ball was going in. I was pleased with the way we played. You could say it's an opportunity missed but we were unfortunate. We had a lot of opportunities and we didn't manage to score.
"Apart from the first 20 minutes, I was very pleased. Once we changed our shape I thought we dominated. We passed it well and create opportunities."