Chris Smith scored the only goal of a tense game in the second half but Barnet's 2-0 defeat at Northampton meant the Daggers survived.
"We've achieved our goal but it's not been the best of days really," said Burnett.
"It's been quite an amazing day. We've been beaten and yet stayed up.
"A lot of the lads looked a bit edgy and I can understand that. We've looked that way on a number of occasions recently.
"We had this result coming in a lot of ways.
"There's always been that work ethic there and the effort from the players has never been an issue for me - it's just the quality hasn't always been there.
"It hasn't been there often enough and in this division any silly mistakes can be punished quite severely.
"That's certainly been the case here. We switch off at the wrong time and the result is that you go home with nothing.
"There's a lot of work to be done before the start of next season, make no mistake about that."