Despite taking the lead in this one and missing some good first half chances, they could have no complaints at the final result - a fact acknowledged by manager Mike Newell who could not celebrate his 44th birthday with a victory.
Grimsby scored a good 19th minute goal when a defensive error let in on-loan midfielders Dean Sinclair and Stuart Elliott and after the former had rounded the keeper, Elliott knocked the ball into the empty net.
But the Mariners' position could have been a lot stronger as strikers Peter Bore and Adam Proudlock both missed when clear on goal.
After Grimsby had repeatedly given the ball away they were made to pay in the 39th minute when Daggers equalised.
Grimsby midfielder Nathan Jarman showed some neat skill but then gave the ball away to striker Ben Strevens who worked it on to Jon Nurse and he beat keeper Phil Barnes from the edge of the box.
After a promising first half on a cold night with a swirling wind the game petered out after the interval with scarcely a chance at either end.
It was Dagenham who looked the likeliest winners and midfielder Solomon Taiwo had three attempts, twice being denied by Barnes and then volleying over.
Grimsby ran out of steam and created nothing in the second half although the crowd did their best to urge them on for what would have been a third successive victory.