Wenger's men prevailed 3-1 at the Emirates Stadium, not before the clash was pushed back by one hour to 21.05 BST because of crowd congestion in London.
A reported 20,000 Cologne fans descended on London despite only 3,000 tickets being available, while some German supporters made their way into the home end as riot police were deployed inside and outside the stadium.
Speaking after substitute Sead Kolasinac, Alexis Sanchez and Hector Bellerin ensured Arsenal got off to a winning start in Group H following Jhon Cordoba's stunning 40-yard opener for Cologne, Wenger told reporters: "We waited patiently in our dressing room but what was difficult for me was that I had all kinds of plans to think about.
"Do we play tomorrow? At what time do we want to play? Do we play next week? But they have a Bundesliga game midweek, we have a League Cup game midweek. Do we move it to Tuesday and play Thursday? It was all kinds of speculations that we had to analyse.
"In the end, at some stage, I thought they will not play the game. I can't see the police taking any risk. We live in a society of 100 per cent security.
"I thought they would never take a gamble to play this game when I saw the images around the stadium but I must say our supporters dealt well with the situation. There was no aggravation and I hope everything goes well after the game.
"Was it the right decision? If nothing happens after the game, yes.
"[The Cologne fans] were very clever. I don't know how they managed to infiltrate our fans and get everywhere but they did that very well. I don't know did they go through Arsenal membership, on the internet. But they did very well."