The visitors wasted two glorious openings early on through captain Abu Ogogo before the Minstermen rallied to take control.
A win would have seen Dagenham climb to within one point of the play-off places and Burnett feels the missed chances have cost his side dearly.
"I didn't see the result coming, but goals change games and that's exactly what has happened," he commented. "I'm actually distraught if I'm being honest. I feel absolutely gutted because in the first half we could have been two or three goals up.
"But they've scored through a mistake that came from us and from then on you are chasing the game.
"Maybe I've asked too much of these players, we've had a tough Christmas period but then so has everyone else. But I'm just very disappointed; it's the most disappointed I've been for a long, long time.
"I really feel we should have won the game. When you make a mistake and it costs you a goal, you have to regroup. Instead we gave a second goal away and I'm a little bit embarrassed for some of the mistakes we made today."