Arsenal failed to get the point they needed to guarantee topping Europa League Group H as Cologne beat them 1-0 in Germany -- but they finished first anyway as Red Star Belgrade and BATE Borisov drew 0-0.
The hosts made a bright start and almost opened the scoring after five minutes when Jhon Cordoba fired in a fierce cross-shot that Arsenal keeper David Ospina pushed away at full stretch.
But the visitors quickly mustered a threat of their own as Francis Coquelin tried his luck from the edge of the area, with the ball whistling wide.
Shortly after the quarter-hour mark, Mathieu Debuchy looked for Danny Welbeck, only for the cross to narrowly elude him, and Calum Chambers ventured forward but scuffed his strike from a promising position.
Cologne tried to step up the pace but Arsenal came forward again and Jack Wilshere sent a bouncing header straight at Timo Horn before Coquelin beat the keeper Timo Horn only to see his effort cannon back off a post.
The home side were forced into a change when captain Dominic Maroh appeared to injure a hamstring in a challenge with Welbeck and was replaced by Konstantin Rausch.
Arsenal boss Arsene Wenger made a change of his own at the break, replacing Welbeck with Alex Iwobi, but his side soon had something to worry about when forward Sehrou Guirassy found himself unmarked on the edge of the area only for Ospina to stop his tame effort.
But soon after the hour, Guirassy won a penalty for Cologne when he went down under the challenge of Matthieu Debuchy, getting up to blast home and give the Bundesliga side the lead.
Per Mertesacker had a header from a corner puched away by Horn before Reiss Nelson came on for Chambers as Wenger made another change.
Arsenal were struggling to create clear chances against a disciplined defence, but as the game entered its final quarter of an hour, a fine pass from Wilshere gave Oliver Giroud the chance to run through only for a heavy first touch to scupper the opportunity.
The visitors brought on striker Eddie Nketiah for Debuchy, but despite late efforts from Reiss and Wilshere, both of whom were denied by Horn, Cologne kept their hopes of progressing intact.