County's Chris Zebroski missed a penalty with the visitors leading 1-0, but Edinburgh believes that his entire team needs to rediscover their winning mentality.
"We cannot keep saying the luck is not with us, we have had enough opportunities but we have not taken them," BBC Sport quotes him as saying.
"We have to realise that the situation we are now in is very difficult. [The penalty miss] was massive. It's one-all and a completely different game.
"Even after 2-0 we have hit the post and then gone in at half-time at 2-1. Credit to the players because we have shown the effort and the commitment, but we have to show more than that now. We need more quality, a little more guile and know-how to rediscover how to win a football match."
The result sees Dagenham climb to 11th place in the table, while County remain in 14th.