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."

The acceptance of the deal by unions will clear a big hurdle for the service which was due to begin last September.
The RMT's 10,000 members will start voting on 11 February.
The Night Tube service will take place on five lines - Jubilee, Victoria, Central, Northern and Piccadilly lines - on Fridays and Saturdays.
More on this story and other news from London
The proposed agreement includes a 2% pay rise in year one, RPI inflation or 1% (whichever is greater) in years two and three, and RPI plus 0.25% or 1% (whichever is greater) in year four, plus a £500 bonus for staff on lines where the night Tube will run.
But three other unions are still to decide on whether they accept the offer.
BBC London's transport correspondent Tom Edwards said the RMT executive's move was a "big step forward".
The train drivers' union Aslef and TSSA, which represents station staff, are yet to decide, although Aslef is said to be "looking like they will also accept".
But Unite, which represents engineering staff, has turned down the offer and wants further talks, Tom Edwards said.
The RMT union is still in talks with London Underground over a planned strike this weekend over the issue of job losses.
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.
[NEXT_CONCEPT]
The Rail, Maritime and Transport union will recommend its members accept a pay and conditions deal for the Night Tube service, its executive has decided.