Rotherham's best chance fell to Adam Le Fondre after 34 minutes when he picked up a loose backpass on the edge of the area but his shot was well saved by Barry Roche.
The home side pressed after the break and Kevin Ellison glanced a header wide before Ryan Taylor was also off target.
Danny Harrison's header was cleared off the line by Gary Hunter and Le Fondre's 71st-minute shot was saved by Roche.
The Shrimps completed a dogged defensive display when Danny Adams bravely blocked Ellison's goalbound effort.
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