Aaron Downes scored the vital goal as he headed home Jak McCourt's cross convincingly.
Daggers were denied by the woodwork as striker Rhys Murphy saw his drilled effort bounce out off a post.
John Marquis almost made it 2-0 to the visitors in the 89th minute but goalkeeper Chris Lewington denied him with a smart stop.
It is now just one win in five games for the Daggers, who remain in 10th place in the League Two table.
Burnett said: "I'm extremely disappointed because we've created a lot of chances but not stuck any of them away.
"I just felt that at times we were just making the wrong decisions in particular situations, especially in and around their box.
"We were taking touches when we didn't really need to.
"You can't be doing that at this level, because here we've seen Torquay score and then shut up shop.
"Credit to Torquay, they're a good side. I believe they were in a false position.
"But for us to be in 10th place at Christmas is a good effort. Don't forget this club has come a long way in a relatively short period of time.
"We'll keep plugging away and we'll soon shake this defeat off."