The Daggers' latest defeat means they are in danger of making an immediate return to the Blue Square Premier after last season's title success.
But they battled hard against Paul Ince's in-form side and were unlucky not to share the spoils in an entertaining encounter.
The hosts were unfortunate not to be ahead after only two minutes later when Paul Benson hit the post.
But the Dons responded well and scored the only goal of the match midway through the first half when Drissa Diallo headed Dean Lewington's corner home.
After Diallo's goal, the Daggers began to get on top and Jon Nurse went close to grabbing an equaliser before half-time when he somehow failed to turn Sam Sloma's free-kick into the net.
After the break John Still's side continued to press and substitute Chris Moore missed a great chance to score with 14 minutes left, before Nurse hit the crossbar.
The visitors should have doubled their lead in stoppage time when Colin Cameron won a penalty only for Dagenham keeper Tony Roberts to pull off a brilliant save from Lloyd Dyer's spot-kick.