An own goal from Abu Ogogo gifted Cobblers a 36th-minute lead, with Sam Williams squandering a couple of good chances for the visitors either side of the opener before Chris Hackett quickly doubled Northampton's advantage.
Matt Saunders and Brian Woodall both then went close for the Daggers before Kelvin Langmead put the result beyond doubt for Town seven minutes into the second half, with Scott Doe finally reduced the arrears in the 71st minute.
"I thought we were not really up and at it and I don't actually think we were in the game," boss Still said.
"Despite not playing well I felt we dealt with everything they had - long throws, corners - I thought we did okay. A different team came out the second half and we could have been 3-2 up before they got their third goal.
"For the third goal the boys just said it came in, it's been whipped in, it's hit someone and gone in. We've gone from being really secure defensively, not the back four, just as a team, to not being secure.
"It's the make-up of the team that can determine how the opportunities come around and the make-up of our team in the first half wasn't good enough.
"We never played the way we know we can play, but in the second half we did. If you play that way for 90 minutes and you get beat you say 'okay that's fair enough, we played our bit' but we haven't played our bit for 90 minutes."