The Grecians looked to be on course for another defeat before Eliot Richards capitalised on goalkeeper Chris Lewington's fumble to bundle the ball home.
Tom Nichols had given Exeter the lead but Dagenham hit back early in the second half through Luke Norris and a contentious penalty scored by Medy Elito.
Yet despite the late setback, Burnett felt there were positives to take from his side's performance.
"Being 2-1 up with 90 seconds to go, is a bit hard to take, but it is football, you have to accept it," he said.
"I said to the players 'be disappointed with the result but don't be disappointed with the performance'. We have got another game on Tuesday and we have to go again.
"It is not an easy place to come to. I know they have not been on the best of runs of late but I have got a lot of time for Paul Tisdale (Exeter boss). He has done an exceptional job at this club, they produce players and continue to produce winning teams.
"I felt we played quite well. We moved the ball well but relinquished possession a little bit too easily. It was a decent match, it was nice to watch two teams try and pass the ball and play football in the right way.
"They scored late on and they will feel like it was a winner. We came here to win, we set out to win the game. The first half we were better than them, we had the better chances and looked more threatening."