The goalless draw in the other Group H game in the end saved Arsene Wenger from a nervous final game after Arsenal failed to secure the single point they needed to guarantee them a place in the better half of the draw next month.
But two nights after Tottenham conquered Germany with a win in Dortmund, this lacklustre capitulation again suggested Arsenal could learn a thing or two from their north London rivals about blooding young talent.
Wenger was always going to make wholesale changes, and perhaps that is where he is going wrong. Without the skeleton of a senior side that Mauricio Pochettino insists on to guide the kids, too much weight of expectation is put on young shoulders.
Yes, this is supposed to be a learning process, but too many of the lessons last night were negative ones.
Welbeck, we discovered, is still only good for 45 minutes. There were glimpses of his effortless acceleration, but all the while he cannot manage longer in such a slow-paced encounter, he remains too fragile for Gareth Southgate even to consider.
"The situation is that it was planned he would only play 45 minutes,” Wenger explained. “He is coming back from injury and we have three more games coming quickly.
"Medically, the risk was high to play longer. He could stay on and was frustrated to come off, but he is in good shape.” Wilshere is another with international aspirations but after dominating the previous two away trips in the Europa League, against Cologne his use of the ball appeared too cumbersome.
The fact that in the first-half Arsenal’s most potent attacking force was Francis Coquelin - a player who has never scored in four years at the club but was inches away with two efforts in the space of 10 minutes - perhaps spoke most of just how badly Arsenal were misfiring.
Indeed, it was not until just after the hour mark that the game woke up. Sehrou Guirassy burst into the Arsenal box and rubbed shoulders with Mathieu Debuchy before flying to the ground.
It was a soft penalty - “not a penalty at all,” according to Wenger - but Guirassy did not let that bother him, smashing the ball into the back of the net.
Belatedly, Arsenal showed a sense of urgency. Wilshere had a shot saved then headed over from close range.
Giroud, clear on goal, took an age to bring the ball down off his chest and was all too quickly thwarted by a pair of Horns, Cologne goalkeeper Timo Horn and defender Jannes Horn.
It was only the introduction of Reiss Nelson that sparked real life into the visitors, his running at players mirrored only by Ainsley Maitland-Niles and Eddie Nketiah.
"Maitland-Niles was very good in the first half and Nelson looked dangerous going forward, the really young players did well on that front,” Wenger said.
"I believe we had a lot of possession and we lost a game when Cologne have one shot on goal. We missed a bit in the final third, some accuracy in our passing to score. We had plenty of danger situations but lacked something.” Which brings us back to some cool heads to guide the younger players. Their energy was impressive, some of the decision-making, understandably, was less so.
When Timo Horn finger-tipped Wilshere’s final injury-time effort over the bar, their fate was sealed. They could not do it themselves: It was very much a downbeat and embarrassed Arsenal that had to thank BATE Borisov and Red Star Belgrade for top place in the group.
"You feel you have done the job to top the group,” Wenger said without enthusiasm. “Now we play the final game with not much at stake beyond wanting to win the game.
"What does finishing top mean? I won’t know until the draw!”
COLOGNE (4-1-3-2): T Horn; Sorensen, Maroh (Rausch 38), Mere; Klunter, Ozcan, Jojic, J Horn; Cordoba (Olkowski 56), Osako (Lehmann 73), Guirassy. Booked: Klunter. Goal: Guirassy 62 pen
ARSENAL (3-4-3): Ospina; Debuchy (Nketiah 83), Mertesacker, Holding; Chambers (Nelson 67), Elneny, Coquelin, Maitland-Niles; Wilshere, Giroud, Welbeck (Iwobi 45). Booked: Debuchy