Kick-off was pushed back by one hour to 21.05 BST due to crowd congestion in London, with a reported 20,000 away supporters said to have travelled from Germany.
Cologne's allocation was set in line with UEFA rules, but thousands travelled without tickets and turned up at the Emirates, with the resulting congestion affecting the ease of entry for home supporters.
Once inside the stadium, some travelling fans are said to have climbed over barriers in order to get into the home supporters' section, where they mixed with Arsenal fans as segregation became impossible for stewards.
After Arsenal's 3-1 win, Arsene Wenger said that he had expected the match to be cancelled, before then admitting that he felt it was the right decision to let the game go ahead as planned as there was "no aggravation".
Arsenal will be investigating, however, to understand how the situation arose and what they can learn from the situation going forward.
"Following last night's UEFA Europa League match with Cologne we would like to stress that fan safety was always our paramount concern and informed all decisions made," the Premier League club said in a statement.
"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.
"This included a number of measures including ensuring no tickets were sold via general sale and that no red memberships purchased after the draw were able to be used to get tickets in the home end for this match. We also worked with our colleagues at Cologne to stop supporters travelling without match tickets.
"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. Many tickets were sold through touts and this is very disappointing.
"We have launched a full review into the circumstances surrounding the game and will ensure any lessons that can be learned are used in the future."