Lee Bell gave the visitors a 34th-minute lead with his fourth goal of the season and first for five games. But man-of-the-match Josh Scott, back at Victoria Road after a loan spell at Ebbsfleet, equalised in the 51st minute with his second goal in as many games to secure a point.
Victory for Port Vale saw the Brewers drop one place in the table to third, with leaders Gillingham also held to a draw.
"I thought we played realty well in the first half, we were the better team," Rowett reflected. "But we conceded a bad goal and that gave Dagenham a lift.
"We always knew it was going to be tough coming here but we didn't really kick on in the second half and get that second goal we were looking for.
"It's a shame we've slipped a place in the table but there's still a hell of a lot to play for and a lot of games left.
"We've just got to keep going, keep working hard and keep doing what we've done so far this season to get us into this great position.
"I thought we scored a good and had some good chances to get a second, but at one-nil you will always give the opposition a chance of getting back into the match."