Matt Partridge headed the hosts into a 20th-minute lead when he nodded home Frankie Raymond’s corner.
Raymond also had a hand in the next two goals, setting up Jamie Cureton just after half-time before netting a free-kick 23 minutes from time.
Jodi Jones struck in the 90th minute to seal victory and leave Currie a very happy man.
“I’m extremely pleased. Obviously we played some nice football which we’re happy about. Some nice names on the scoresheet which will please everyone,” he said.
Dagenham began brightly, dominating the early exchanges which again pleased Currie.
“We started very well. We just lacked that little bit of cutting edge in the final third. Eventually it came with a great ball in by Frank and a great header by Matty. We were onto the next sort of level. We were quite dominant today and I thought we were quite comfortable.”
Cureton came off the bench to score, replacing Ade Yusuff who came off injured midway through the first-half.
“This is what we’ve come to see week in week out from Curo. He’s a nuisance,” added Currie.
“Ade’s a bit more physical whereas Curo’s a bit more clever. You never know where he is. He never gets in physical battles. That’s not the player he is.
“When the ball is put through like that and he has the half a yard on someone, the net will bulge and thankfully it did.”
Raymond was only making his second start for the club, having impressed last week against Newport, and Currie believes there are promising signs from the youngster.
“Frank was brilliant,” he said. “He’s bullied a few out of the way to take the free-kick and it was nice to see it go in. To be fair to him he does practice them, he’s got a nice enough foot.”
Accrington boss John Coleman was frustrated his team failed to reward the travelling support with a good performance.
“You’ve got to take your hat off to Dagenham who were miles better than us today,” said Coleman.
“We were second to every ball. We defended atrociously and we got exactly what we deserved. I’m sorry for the fans who made the effort and were in good spirits all game. I thank them for coming but want to apologise. We didn’t mean to do that.
“I don’t think the players have turned up thinking we were going to play badly today but we came up against a team full of confidence. The goals we conceded at important times derailed us really. They were poor goals to concede.”
“It looked like an end of season game where one team looked jaded. They looked up for it. Sometimes you can’t put your finger on it.”