Arsenal blamed the selling of tickets by touts for the crowd problems at Thursday's (Friday AEST) game as UEFA began disciplinary proceedings on Friday (Saturday AEST).
Cologne meanwhile were playing in Europe for the first time for 25 years with an estimated 20,000 descending on London for the clash.
The Budesliga club criticised the security for the event and questioned why only 3,000 were allocated for away fans at the 60,000-seater Emirites Stadium.
Cologne and Arsenal have been charged with various offences at the match which was delayed by an hour after large numbers of German fans descended on the Emirates Stadium, the majority of them without tickets.
Many bought tickets for areas of the stadium occupied by Arsenal supporters, causing segregation issues, although there were only isolated incidents of trouble once the game started.
Cologne criticised Arsenal's security and felt the police presence was not sufficient.
Arsenal said they had worked with the Metropolitan Police and UEFA in deciding whether the game, which the English team won 3-1, went ahead.
"Following last night's match we would like to stress that fan safety was always our paramount concern and informed all decisions made," Arsenal said in a statement.
"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 kickoff.
"Many tickets were sold through touts and this is very disappointing," the club added.
"We worked in full consultation with police and UEFA officials on the night and in advance of the game and had taken extensive steps in advance to prevent tickets being sold to visiting supporters."
UEFA said Cologne had been charged with crowd disturbances, the setting off of fireworks, throwing objects and acts of damage to the stadium.
Arsenal were charged with a breach of safety and security regulations because of a blocked stairway in the away end, European soccer's ruling body said in a statement.
Arsenal have launched a full review into the circumstances surrounding the game.
They denied claims that some Cologne fans had acquired tickets by joining Arsenal's membership scheme.
"No red memberships purchased after the draw were able to be used to get tickets in the home end for this match," Arsenal said. "We also worked with our colleagues at Cologne to stop supporters travelling without match tickets."
Cologne apologised for the behavior of their fans but were critical of the event's origination.
"The security concept and communication seemed inadequate and the police force too small," Cologne said in a club statement.
"Due to the enormous demand for tickets, it would have been sensible, not least for security reasons, to allow more than the allocated five percent of stadium capacity to the guest fans."
On the situation before the match, the statement added: "Despite the tremendous experience of both the London security forces and Arsenal as a permanent partaker in European football, the organisers were unfortunately not adequately prepared for the task."
Police said five people had been arrested, all on suspicion of public order offences.
UEFA's Ethics and Disciplinary Body will deal with the case on Thursday.