Grimsby pressed to break the deadlock when Pat Hoban struck from range and Andy Monkhouse headed wide.
Darren Carter came close for the hosts but hit the side netting after rounding the Grimsby backline.
Disley headed home to seal three points with 19 minutes left when he converted Monkhouse's cross from the left wing.
Forest Green boss Ady Pennock told BBC Radio Gloucestershire:
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"Obviously we're disappointed and I didn't think we tested their keeper enough, Stevie Arnold made three or four good saves, but the game should have been 0-0.
"I didn't think in the final third we were that great, but all credit to Grimsby they've done a good job on us and won the game 1-0.
"It's three points - we're not going to lose the title by losing today and we're not going to not get in the play-offs, so it's three points, that's all it is."
Grimsby manager Paul Hurst told BBC Radio Humberside:
"Second half we had to withstand some pressure without James McKeown really being called upon to make any real saves of note, but you know you're going to have to defend a lot of set plays into the box.
"You wondered with their record if they were going to get that late goal but thankfully we kept that clean sheet and sent a lot of fans home very happy.
"Automatic promotion is still a big ask. Its two teams we've got to catch and they don't have to play each other."
Craig Disley scored the only goal as Forest Green Rovers were denied the chance to go top of the National League with defeat by Grimsby Town.