One fan said 300 people were bussed across the airfield to a plane - only to find it had 150 seats.
A spokeswoman for the airport said they were inundated with supporters.
But Fulham fan Dawn Dunlop said the airport was "not able to cope" with the extra supporters.
She told the BBC: "They didn't have enough staff. The whole thing has been a complete disaster."
Ms Dunlop continued: "They decided to bus us out to the plane that was somewhere on the airfield.
Getting back from Hamburg Airport is not straightforward Nick GodwinBBC London match commentator "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'.
There were still problems on Thursday morning.
Nick Godwin, a member of the BBC London 94.9 commentary team, was trying to catch a flight at 0830 BST.
He said: "It has taken forever to check in. There is a massive queue and it may be a computer problem.
"That is nearly 24 hours after the match finished - if they had these problems last night it would have caused a huge problem."
He added: "I have seen three people who have missed their flights already because of the queue. Getting back from Hamburg Airport is not straightforward."
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."
It was Fulham's first ever European final.
Here is a selection of comments from people who had difficulties getting home:
We saw very little staff, there were no announcements made. Fans were being asked to wait en masse, and then sent to other areas where we stood in another mass. There was no orderly queuing because we were all milling around here, there and everywhere. Two passengers collapsed and helping them was difficult because of the chaos. This was on top of the fact that bus transfers were not always satisfactory. I am 76 and like others stood for over two hours as there was nowhere for us to go. Even the drinks dispensers were not fully operational. A few of the coach transfers to and from Hamburg airport had difficulties too.Marjorie Taylor, Morden
It was a complete disaster! They had no clue what they were doing and no information was given. After two hours an announcement came. 'For all the supporters looking to travel to London, please do not worry - the planes only have a slight delay.' Something we clearly hadn't noticed. The explanation which was given was that the planes were all lined up, however they were unable to taxi the planes to the gates or to transport guests in buses to the planes. Upon asking why not, no explanation was given. I arrived at the gate at 12.45am ready to board, however only got a plane at 5am. I was one of the first to fly home because this plane had a lot of children on board. They just left us sitting or lying on the floor for four hours without supplying anything, but earning money from supporters buying drinks and food - an easy way to make money!Jeroen, London
My flight was due to leave Hamburg at 0040 on Thursday morning. We had expected this time to be pushed back by half an hour or so because of the extra time but I didn't manage to get out of Hamburg until 2.45am. This was because a free for all had been announced by the airport authority. They told us to 'get on the first plane to Gatwick'. I realise that I was one of the lucky ones. The main problem was getting a bus. At our gate, there seemed to be only one bus transporting all of the fans to the plane. Worse still was the fact that once the bus was full it closed all the doors and waited just outside the gate for 10-15 minutes not doing anything. Then the driver of the bus got out and left us for 30 minutes. I have no idea where he went. When we got to the planes I counted five Jet2 flights sitting on the airfield just waiting for passengers. The crew were almost as livid as we were. Harry Gibson, Reigate
It was chaos at Hamburg airport after the match. We queued for over four hours waiting to get on a bus to the waiting aircraft. There were no reps from the tour companies we had flown out with and the departure boards gave no accurate information. A few posters stuck up on walls were apparently there for us to find out, but thousands walked past them unaware they were relevant. We joined two different queues only to be told eventually we were in the wrong one. We were told that the problem was that Hamburg airport had not got enough drivers to drive the buses of passengers to the planes. It was so shambolic. Having left at full-time and returned to the airport at about 11.45pm German time, I eventually got to Gatwick at 6am.Geoff, Petersfield, UK
The major problem was Thompson sport had its advisers tell Fulham fans that Hamburg Airport were operating a ridiculous open gate policy, and to basically line up at any gate destined for Gatwick. Unfortunately not all reps conveyed this message so you had instances of 500 people lined up at one gate, and 20 at another. There was no communication, the reps had disappeared. I was fortunate to have gone to my original gate which, due to being out of the way, was not as long as the others. Still, despite being one of the first planes to leave we didn't arrive in Gatwick until just before 4am. The 'open gate' policy was absolutely the cause of the chaos. Combining that with woeful communication is the single reason why this happened.Aaron James, Balham, London
Planes were scheduled to leave at staggered times between 1am and 5.15am. My flight was supposed to be one of the last to leave which left eventually around 6am but was in fact one of the first. Thousands of fans were left stranded. The airport authority staff walked off the site around 2am and left us to our own devices with no information or help. They had made no arrangement to cope with the large number of fans scheduled to leave that night. There seemed to be no staff to tow the planes onto the runways and no buses to take passengers to the planes. Thompson Sports Travel were locked in negotiation with airport staff for five hours to solve the problem. The airport authority simply had no idea what to do. This city should not host any further football events until further notice and FIFA should investigate. Geoffrey Green, Edenbridge, UK