Despite dominating large spells of the game, the Bees succumbed to a late Stockport winner having been a goal ahead midway through the second half.
HOW IT HAPPENED
An early effort from Ephron Mason-Clark was saved by the visiting keeper Ben Hinchliffe to the centre of the goal straight from kick off.
Strong early pressure from the Hatters as the Bees sought to gain control in the centre of the park.
A sharp through ball from Mason-Clark set Josh Walker through on goal but his effort was well blocked for a corner.
Having worked himself a yard of space, a shot from Ephron Mason-Clark flew over the bar as Barnet began to put some pressure on the Stockport backline.
As the Bees carved Stockport open midway through the first half, Josh Walker was again thwarted as his low effort found the legs of Hinchliffe in the County goal.
After clearing the area from a Hatters set peice, Walker was again clear one on one with Ash Palmer, jinking inside and his left footed finish was saved before David Tutonda's rebound flew over the bar.
With the half drawing to a close, Tutonda found Elito alone on the edge of the area and his shot was headed over the bar for a corner for the Bees.
As the second half began to take shape, a corner from Barnet was cleared to the egde of the area before James Dunne's strike was blocked and the move fizzled out for the Bees.
After good work from Mason-Clark, his lay off to the edge of the area for Harry Taylor was a chance spurned as his effort soared over the Stockport bar.
Midway through the second half, a rasping long range strike from Elito flew just wide of the left hand post as the Bees continued to control the game without breaking the deadlock.
Finally, on 69 minutes the Bees found the net, as Ephron Mason-Clark let fly from 20 yards with his left foot and it nestled into the bottom left hand corner beyond Hinchliffe.
Soon after taking the lead, Stockport almost found an equaliser as Elliot Osborne was released down the right hand side and his low cross was inches away from finding Devante Rodney on the slide.
Attempting to add to their tally, Josh Walker riggled away from a challenge in the box and his strike was blocked and went out for a Bees corner.
With 15 minutes to go, Stockport levelled the scores through Osborne's point blank shot.
Elito tries his hardest to give the Bees the lead once more as his 20 yard effort is inches wide.
A substitution for Barnet saw Okem Chime replace Tutonda to make his league debut after impressing in the U18's in recent weeks.
With 5 minutes of normal time to play, Rodney cut inside towards the Barnet goal, and attempted to round the onrushing Scott Loach in goal for the Bees, but he was able to smother the ball and set his side on the attack.
As the game became stretched, Stockport's Osborne's curling effort was just wide and from the resulting corner Mulhern bundled the ball home to give the Hatters the advantage in the 89th minute.
The Bees will feel mighty hard done by not to take anything from a game that they dominated for large spells.
ATT: 1536 (405)
Mauro Vilhete and Jack Taylor dropped out for the Bees, with Ephron Mason-Clark and Medy Elito replacing them in the lineup.
WHAT IT MEANS
With the game going against the Bees, the result sees Barnet drop down to 14th in the National League, with Stockport rising to 10th.
Barnet are away at Barrow on the 23rd of November for a 3 o'clock kick for the Bees at the Holker Street Stadium.