Stuart Fleetwood opened the scoring for the home side with a brilliant curling shot from 25 yards, but poor goalkeeping from Paul Jones allowed Daggers striker Ben Strevens to net an equaliser.
However, Fleetwood won it for Exeter with his second goal - a stunning dipping volley from 25 yards after he turned sharply on a Matt Gill throw - to cement the Grecians' place in the top three.
"I thought we were beaten by two great goals," Still said. "Did we have the edge? Maybe. It was quite even.
"I thought the lads put in a terrific performance but were undone by two terrific strikes. It was a close game, but the quality of the finishes was first class and that is every credit to Stuart.
"They really were two high-quality goals, but the level of performance
from us was first class. We still need four wins and I will never lose sight of who we are. We are Dagenham & Redbridge and to even be talking about it is dreamland for the club and for me."