Adam Le Fondre (who else) netted the only goal on the hour mark, but the Millers had to defend deep at times to stave off Daggers' physical threat.
Moore was a happy man though as he spoke to the post match media.
He said afterwards: "It was a fantastic team performance.
"I thought in the first half we passed it well but we didn't threaten too much in the attacking third. We spoke about it at half time, Alfie then got the goal and after that I thought we were comfortable.
"They threw bodies forward and pumped long balls and throw ins into our box but we dealt with it and defended magnificently. If we defend like we did today then we will be in third spot, there is no doubt about that."
Of new signing Craig McAllister, who arrived from Exeter on Thursday, Moore added; "I thought he did well.
"It was hard for him and you can see that he hasn't played many games but he was clever, he knows his centre forward role. I felt that he held the ball up and he linked up very well with Alfie at times.
"He only came in on Friday so there is plenty more to come."