Millwall boss Kenny Jackett has admitted his side's problems in front of goal have cost them this season and once again they drew a blank despite having the bulk of possession.
Jackett has brought in Tottenham youngster Harry Kane in a bid to find a cutting edge, but he was once again without top scorer Darius Henderson through injury.
Kane and strike partner John Marquis had plenty of half-chances but the Championship side could not find a way past Dagenham goalkeeper Chris Lewington and will now have to have another crack at The Den.
In a scrappy opening, Kane had the first opportunity with a shot which Lewington held.
Millwall, who have won away just once in the league this season, should have taken the lead just before the half-hour mark when Liam Trotter played in Liam Feeney but the winger dragged his shot wide.
Lewington then saved from James Henry, Kane planted a header over, and Marquis drilled an effort high and wide with the Lions beginning to take control.
Dagenham's only opportunity of the first half fell to Oluwafemi Ilesanmi, who blazed a couple of yards over after a quarter of an hour.
Millwall survived a minor scare just after the interval when goalkeeper Steve Mildenhall miskicked a backpass but Brian Woodall could only cross the ball into an empty goalmouth and the chance disappeared.
At the other end Marquis fired wide again, Kane headed Scott Barron's cross straight into the arms of Lewington and Darren Ward's header was blocked by Abu Ogogo.
Trotter should have broken the deadlock on the hour from another Barron delivery but put his header inches over the crossbar.
Millwall thought they could have had a penalty when Trotter tumbled in the area but referee Graham Salisbury was not interested.
Trotter then played in substitute Josh McQuoid but his effort was deflected wide.
One bright spot for Millwall was the return of striker Shaun Batt as a late substitute, 18 months after he suffered a cruciate injury in a pre-season friendly.
For Dagenham, Jon Nurse's header was saved by Mildenhall and Millwall skipper Paul Robinson had to block a shot from Billy Bingham.
But neither side was capable of making a breakthrough on a blustery afternoon, and the Daggers will now make the short trip south of the river after securing a hard-earned replay.