The Gunners ran out 3-1 winners in the Group H opener, which was delayed by an hour after away supporters caused havoc outside the stadium.
As many as 20,000 Cologne fans are believed to have made the journey from western Germany despite only 3,000 tickets being made available.
That meant many attempted to enter without tickets or with tickets for the Arsenal sections, where it soon became clear ahead of kick-off that plenty had succeeded.
Five arrests were made as the Metropolitan Police said that additional officers had been deployed to the area following the unrest.
During the game, Cologne fans clashed with stewards, brought in flares and sat in home sections but it is likely to be Arsenal – as organisers of the match – who face potential sanctions.
However, Stoger opted to refuse to discuss the matter following the game and said: “I have no comment about the fans.
“I’m the coach, my job is the team, my job is football not the fans.”
A club spokeswoman added: “We have to first inform ourselves and in the next few days we will talk about that.”
Jhon Cordoba’s long-range effort had put Cologne ahead in the first half, but substitute Sead Kolasinac volleyed Arsenal level before Alexis Sanchez and Hector Bellerin struck to seal the three points for the hosts.
England manager Gareth Southgate has claimed that the country needs to boot racism out of its own football before criticising World Cup hosts Russia.
Newcastle have been linked with a shock move for former Sunderland goalkeeper Simon Mignolet during the summer.