The Gunners, showing 11 changes from Saturday's north London derby success over Tottenham, were beaten 1-0 in a poor contest at the RheinEnergieStadion.
A controversial second-half penalty settled the tie as Mathieu Debuchy was adjudged to have fouled Sehrou Guirassy in the area when there was minimal contact.
Guirassy stepped up to convert the resulting spot-kick and give Cologne the three points which keeps them in the hunt to go through with Arsenal in second place.
Wenger's side still progress as Group H winners despite the defeat and there was more good news for Arsenal fans as the Frenchman revealed the plan was always to withdraw Welbeck, playing his first game in a month following a groin injury, at the interval.
"It was planned before the game that he would only play 45 minutes," he said.
"He has only just come back from injury, and we have three more games on Sunday, Wednesday and Saturday again.
"Medically, the risk was a bit too high to play him for longer because he has been out for a while
He has no problem.
"Of course, he was ready to stay on and frustrated to come off, but he's in good shape."
Wenger was not amused by the decision of Russian official Vladislav Bezborodov to award what turned out to be the match-winning penalty but did praise the hosts, who sit bottom of the Bundesliga without a league win all season, for their defensive resilience.
"We had a lot of possession," he added.
"We lost the game to one shot basically
It was a very nice penalty that we have to take on board
It was honestly not a penalty at all.
"We missed a little bit of the 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.
"I must also say that Cologne defended with spirit, with commitment and overall the crowd was absolutely fantastic for them."
Cologne boss Peter Stoger has come under pressure following their poor domestic form but back-to-back Europa League wins will help his cause and the Austrian was delighted with his side.
"It was a battle - a hard-fought win," he said.
"The passion and fight for this game was there
I was incredibly impressed with my side
The lads are shattered after giving it their all
I'm proud of them and delighted we could take something from this game."
Source : PA