With only one win since Moore took charge of the club for the second time six games ago, it was Aldershot who looked the more likely in a game that fizzled out to the only scoreless match of the day in the division.
It was the visitors who opened up the Millers defence from the off, when Jon Grant and Kirk Hudson combined well before Grant's effort was cleared following a last ditch Pablo Mills tackle.
Shots 'keeper Mikhael Jaimez Ruiz was called into action on seven minutes as Kevin Ellison set up Tom Pope who's shot was well saved from inside the 18 yard box.
Ruiz was also down smartly moments later to stop an Andy Nicholas header from Ellison's corner right on the line.
Grant came close to opening the scoring on 15 minutes after Lewis Charmers beat Dale Tonge in an aerial battle, but Grant's shot on the stretch went wide of Andy Warrington's upright.
Tom Pope then saw an effort go over the bar from Paul Warne's centre and the Shots' Scott Donnelly's 20 yard curler failed to trouble Warrington at the other end.
Pope then flashed a header over the top from Ellison's corner in first half stoppage time.
The second half began with the Millers switching to 4-4-2 with Kevin Ellison shooting wide from long range.
The Millers began to come back into the game a touch but the Shots created the best two scoring opportunites of the half as Warrington tipped Adam Hinshelwood's header over on 64 minutes.
Then Donnelly came within inches of breaking the deadlock as his 20 yard free kick rebounded off the foot of the post before Ian Sharps' header from a Warne corner forced the best save of the half from Ruiz as he parried the ball to safety.
Marvin Morgan could have won it late on for the visitors but after being played in by Hudson, the substitute scuffed his shot.