Newport suffered a second successive home loss at Rodney Parade after they were edged out in a remarkable late flurry of five goals in the final 13 minutes.
Newport-born striker Christian Doige and Alex Jabubiak struck for Dagenham. David Tutonda and Aaron O’Connor replied late on but was not enough to step the Exiles slipping three points off the play-offs.
Dack said: “We should have taken our chances when it was 0-0 but we didn’t take them and they went down the other end and took their chances. That’s been the story of our last six games.
“It’s easy scoring two goals when the pressure is off and that’s what it boiled down to. We lacked quality in both boxes but once we’re losing 3-0 it’s easy to do it then. The pressure got to the players.
“The positives are that we have got 62 points, we only got 58 last year. Are we a play-off side? Well, we’ve had chances in our last four games and we let them slip.
“The future is rosy, though, and we’re going to run with a few of the younger guys now. The players need to go out there and play with freedom. We’re going to fight to the end and see where it takes us.”
Defeat capped a miserable week for Newport just a day after they sacked disgraced striker Chris Zebroski, who was jailed for four years for assault and robbery.
After a quiet first half the Exiles almost broke the deadlock when Aaron O’Connor’s shot brought an astonishing save from the visitors’ keeper.
Mark Cousins tipped the shot onto the woodwork and was on hand two minutes later to deny youngster Regan Poole.
The game burst into life in the 78th minute when Daggers midfielder Hemmings headed home Andre Boucard’s free-kick.
The visitors doubled their lead three minutes later when substitute Doidge calmly slotted past Joe Day before Jakubiak made it 3-0.
Goal-scorer Doidge was thrilled to have a hand in securing all three points on return to his hometown.
He said: “It was absolutely amazing, I had a couple of friends in the crowd so it was nice to score in front of them.
“I was a bit nervous at the end when they scored two goals but we were never going to lose that game after scoring three goals.
And Doige is determined to earn his place in the starting XI after an impressive cameo performance.
He added: “I’ve just got to be on my toes now and work hard in training.”