The 24-year-old former Millwall frontman thought he had opened the scoring for the Millers after 38 minutes, only for referee Andy Woolmer to rule it out for handball and book him in the process.
Gillingham had chances to go in front before then but neither Jo Kuffour or Curtis Weston could convert, while Grabban was also wasteful after the break.
With just 15 minutes on the clock Paolo Gazzaniga's goal-kick left Michael Raynes confused, with the Rotherham defender directing the ball to Kuffour - but he smashed his one-on-one shot wide.
Weston scuffed a rebound agonisingly wide moments later after Rotherham goalkeeper Rhys Taylor smothered Gavin Tomlin as he burst through before Grabban's disallowed effort.
Grabban was in action again after 64 minutes but could only head across goal, while strike partner Alex Revell couldn't test Gazzaniga either as it end goalless.
