Despite losing, the Gunners still finished top of Group H after rivals BATE Borisov and Red Star Belgrade played out a 0-0 draw.
The Cologne goal came from a Sehrou Guirassy 62nd-minute penalty after the same player was adjudged to have been fouled by Mathieu Debuchy.
The Gunners second-string side had plenty of possession on the night, but could not find a way through, much to the disappointment of Wenger.
"We missed a little bit of accuracy in our passing in the final third that is required to score more goals. We had plenty of dangerous situations, but we always missed a little something to finish our chances," he said.
"I must also say that Cologne defended with spirit, with commitment and overall the crowd was absolutely fantastic for them."
In typical Wenger fashion, he disagreed with the spot-kick decision that cost Arsenal the game.
"We had a lot of possession. We lost the game to one shot, basically," said Wenger.
"It was a very nice penalty that we have to take on board. It was honestly not a penalty at all."