The Silkmen have now scored just two goals in seven league games and must be grateful to their strong defence and resolute keeper Jose Veiga.
The game came alive in the 16th minute when Jon Harley saw a dipping 40-yard volley tipped over the bar by Veiga, who again proved his worth in the 25th minute when he threw himself to the right to clutch onto a powerful Alex Revell drive.
Colin Daniel produced Macc’s first shot on target in the 41st minute, but his fierce shot from 25 yards was punched clear by Conrad Logan.
Three minutes after the break the athletic Veiga brilliantly plucked a Lewis Grabban header out of thin air.
Macc wasted the best chance of the game in the 74th minute when Donnelly sent a free header from six yards tamely wide.
Millers sub Brett Williams nearly won the game in the 89th minute when his rifled 20-yard effort cannoned back off the crossbar.