One fan said 300 people were bussed across the airfield to a plane - only to find it had 150 seats.
Dawn Dunlop told the BBC: "They didn't have enough staff. The whole thing has been a complete disaster."
Fulham were beaten 2-1 by Atletico Madrid in their first ever European final.
Ms Dunlop said the airport was "not able to cope" with the extra supporters.
She continued: "They decided to bus us out to the plane that was somewhere on the airfield.
"Three hundred people were taken out - but there were only 150 seats."
Fellow fan Lyndon Morant posted a photo on social-networking site Twitter of long queues at Hamburg Airport entitled 'Fulham fans in chaos'.
A spokeswoman for Hamburg Airport said: "We had 100 planes extra and 25,000 supporters came.
"After the game within one hour they were at the airport and wanted to go at once to their planes - it was a big task."
She continued: "We had 1,500 people there to look after them. But one or another of the tasks may have gone wrong."
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Source: BBC Sport
Source: BBC Sport