The visiting Daggers took the lead after just five minutes when Shaun Beeley was adjudged to have handled inside the penalty area, Medy Elito converting the resulting spot-kick.
But Town levelled just a minute later - Junior Brown may have intended his ball from the right channel as a cross, instead it crept in at the back post.
Winger Gareth Evans then completed the turnaround early in the second half when he cut in from the left and fired home an unstoppable 20-yard shot.
Burnett said: "We didn't work their goalkeeper enough. But we controlled a lot of possession.
"I think they had one shot second half. It was a screamer, but I'd like to be able to take one shot and win a game. It wasn't meant to be.
"I felt we played okay, not great, but probably didn't threaten them enough.
"We made two changes, just to liven things up, to give people some hope. You make substitutions, sometimes it works, sometimes it doesn't.
"It didn't work and I'm bitterly disappointed because I think we were good enough to get something out of the game."