A fourth successive defeat on German soil did not prove too damaging for the Gunners, though, as closest challengers Red Star Belgrade were held by BATE Borisov elsewhere tonight, meaning that they will still finish top of the standings.
Arsenal were the side looking more likely to open the scoring as the half-time whistle approached, as Francis Coquelin sent one shot wide from 20 yards and another against the outside of the post from a slight angle.
Arguably the best chance of the lot fell Jack Wilshere's way, however, heading the ball into the hands of Horn after being picked out by a Maitland-Niles cross.
Arsene Wenger withdrew returning forward Danny Welbeck at half time and instead turned to Alex Iwobi, but the fresh legs did not equate to fresh ideas as Arsenal struggled to create clear-cut openings.
Koln wasted a good opportunity to make the breakthrough on the hour, with Guirassy failing to find a way past Ospina from a promising position, though the young striker was granted a chance to redeem himself soon after.
Following a tangle of legs with Debuchy inside the box, the referee controversially pointed to the spot and Guirassy smashed the ball down the middle to give the Billy Goats a huge goal.
Per Mertesacker and Wilshere provided the best of Arsenal's attempts in the 10 minutes that followed as the visitors stepped things up, and Wilshere also glanced over the bar from a right-sided cross.
The Gunners, with just two defeats in their last 15 matches overall heading into this clash, then saw Olivier Giroud and substitute Reiss Nelson squander chances in the remainder - the latter weaving through but being denied by Horn.
From the final meaningful chance of the match, Horn helped Wilshere's shot over the bar to give the hosts - still without a league win to their name this term - real hope of overtaking Red Star to finish second in Group H.