Cologne criticised security arrangements at Arsenal on Friday after both clubs were charged by UEFA following chaotic scenes that marred their Europa League clash at the Emirates Stadium.
Visiting supporters were issued with around 3,000 tickets for Thursday's Group H match but about 20,000 fans of the German club are believed to have made the journey to the British capital.
The start of the game was delayed by an hour as ticketless Cologne fans tried to gain entry to the ground in north London and there were clearly thousands of away supporters sitting among Arsenal fans, causing a security risk.
The Metropolitan Police said five people had been arrested on suspicion of public order offences and three officers had been injured as a result of the disorder, none of seriously.
The German club said in a statement: "Too few places were attributed to FC Cologne supporters because five percent of the total capacity of the stadium was not sufficient. It was predictable that several thousand supporters would try to get into the stadium by any means possible."
Cologne, who said the troublemakers had "caused severe damage" to the club, also criticised security arrangements at the Emirates.
"Despite the immense experience of the London security staff, who are used to Arsenal's regular European matches, those in charge did not sufficiently prepare for the event.
"The entire security plan and the communication around it appeared to us to be insufficient and there were not enough police on duty."
The German club added: "Although FC Cologne bear no responsibility for the acts of these troublemakers, we apologise to our English hosts."
Both clubs now face disciplinary proceedings from European football's governing body UEFA.
Cologne fans are accused of crowd disturbances, setting off fireworks, throwing objects and causing acts of damage, while Arsenal face a probe for "stairways blocked in away supporters sector".
- UEFA charges -
UEFA said it would deal with the cases on September 21.
YouTube footage showed thousands of Cologne fans surging through the streets of London before the match, chanting and setting off flares.
Arsenal said they had launched a "full review into the circumstances surrounding the game and will ensure any lessons that can be learned are used in the future".
Manager Arsene Wenger said he was surprised the game went ahead.
"I thought they would not play the game, because I can't see the police taking any risk," he said.
"We live in a society of 100 percent security and 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 as well dealt well with the situation and there was no aggravation."
Cologne goalkeeper Timo Horn said the small minority of fans who misbehaved had "brought shame on the club".
Arsenal's statement also said it was "very disappointing" that so many home tickets appeared to have been purchased by Cologne supporters via ticket touts after the club worked closely with police, who deployed extra numbers once the trouble began, and UEFA.
"The 3,000 tickets issued to Cologne fans was in line with competition rules but it is clear many more visiting fans arrived, causing significant congestion and disturbance outside the stadium before kick-off," it said.
"Many tickets were sold through touts and this is very disappointing and something we continue to work hard to address."
Arsenal won the match 3-1 after falling behind to a long-range strike from Jhon Cordoba before bouncing back in the second half. Substitute Sead Kolasinac equalised before goals from Alexis Sanchez and Hector Bellerin gave the Londoners the win.
Cologne coach Peter Stoeger refused to be questioned on the actions of the club's supporters, saying: "I have no comment about the fans."
"I'm the coach, my job is the team, my job is football not the fans," the Austrian added.