Visiting striker Phil Jevons saw a 30-yard lob go just wide early on and Ian Craney then fired into the side netting.
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.