Fans paid £300 each for the trip booked through Everton FC Travel Club. They should have boarded an Air Scandic flight but the company collapsed on Wednesday.
The Travel Club, operated by ATP International, was told the aircraft was under lease from Viking Air, who had agreed to operate the flight in place of Air Scandic.
The scheduled pilot had called in sick, delaying it while a replacement was found. But the aircraft was then impounded by East Midlands Airport.
Merseyside Police arrested one fan and confirmed they ejected other supporters from the airport.
Last night, the club announced it would give fans a full refund.
Company secretary Mike Beacher said: "We naturally regret what happened and we can only apologise to those fans who were unable to travel out to Bucharest."
ATP chief executive Graham Ramsey said: "I would like to apologise to all the Everton fans who were unable to watch their team play tonight.
"Everyone at Everton FC, ATP International, Starflight Aviation and Viking Air all worked extremely hard to try and resolve the problem, but events conspired against us."
A spokesman for the airport said: "There had been no trouble at all in the morning but understandably they were very angry when they were told there would be no flight.
"We called the police as a precaution and took the fans to an area near the exit to give them the news for safety reasons."