Murphy drilled home in the second half after Michael Smith's looping header had given the Dons the lead before the break.
The result ends a run of four consecutive away defeats for the Daggers and Burnett admits he was forced into Plan B after midfielder Billy Bingham was injured midway through the first half.
"It was a brilliant finish from Rhys, that's what he does," Burnett said.
"He's scored nine now and is still top goalscorer in the league. He's getting the plaudits and rightly so, but can he be better? Yes.
"I think if we scored the first goal we would have won the game.
"Abu (Ogogo) our captain was missing, Billy Bingham went off and we had Medy Elito in midfield who did brilliantly well.
"I'm delighted that we showed strength of character. We came back at a place which isn't easy to come.
"Sometimes you have to look at it that even though we've been beaten in the last four away games, we haven't played poorly.
"If we were horrendous I'd think we'd need a bit of help.
"Possession-wise, shots on target, predominantly we've been the better team. Sometimes in the face of defeat you can take the positives from it."
The Dons had the best chances to clinch victory with Smith and Harry Pell going close in the second half.
It was the battle of the two number nines - Murphy and Smith topping the Sky Bet League Two goalscoring charts with nine and eight goals respectively - but Dons boss Neal Ardley insists he would not swap his star striker.
"They are two different types of strikers," said Ardley.
"We looked at Rhys in the summer and at the time we were looking for more of an orthodox number nine than one with clever movement.
"But I look at my players and think Michael Smith was phenomenal.
"Once I saw him chase back from the halfway line to put a tackle in on the edge of their box and if your striker puts in the work ethic like that, he could be a very good player if he keeps going.
"Our fans will be part disappointed that we couldn't beat Dagenham at home, but I think that's where both teams are at the moment.
"They're a decent team and I think in that first 10, 15 minutes they put us a little bit on the back foot with their pace and trickery, their movement.
"Sometimes it's like a boxer; you're feeling someone out for that punch."