It means the Gills maintain their 100 percent start to the new season, having won all three of their league games along with overcoming Bristol City in the Capital One Cup.
Myles Weston struck a second-half winner after a penalty from Dagenham's Dwight Gayle cancelled out Deon Burton's opener.
"It was always going to be a tough game with the rainstorms and skiddy conditions," Allen said.
"We deserved to go ahead. There will always be times at Dagenham when they come into the game because that's naturally the way they play.
"In the second half I thought we played with a lot more quality, got on top and everybody in our team defended. They put their bodies on the line and heads in the way and did a fantastic job."