Northwich crashed to their fifth consecutive defeat, but only after hitting the crossbar twice and manager Steve Davis was adamant that the result ought to have been different.
He said: "We deserved to win the game in the first 15 minutes and we also hit the bar twice.
"Turning round two goals ahead would have put a different complexion on the game, but once in front Dagenham kept things tight and we did not get at them enough." The decisive goal arrived four minutes into the second half.
A hotly contested free-kick was swung to the far post by Alan Kimble and Tim Cole rose highest to head home.
On the balance of play Dagenham were the better side, but once in front only created one more chance and that in injury time when Steve Garvey came to the rescue on the goal-line for Northwich when Leon Braithwaite threatened.
The home side started at a furious pace and Tony Roberts had already made one save from Mark Barnard when he was beaten by a right-wing cross from Jon Allan. Chris Ward met the ball which cannoned off the crossbar from close range.
Just before the break Chris Thompson outbattled Cole in midfield and tried his luck from 40 yards only to see the ball skim off the top of the bar.
Northwich only managed one good chance in the second half and substitute striker Dean Butterworth ought to have done much better when Garvey threaded the ball to him, however his shot ricocheted off the legs of the advancing Roberts.