The victims included members of football governing body FIFA's executive committee.
The airport disarray was a rare blemish on the so far successful hosting of the World Cup, held on the continent for the first time, which has gone without any major glitches.
Some VIP planes, which were supposed to land at the new Durban King Shaka International airport and later park at an old airport some 60 km (40 miles) away, would not move, causing the chaos, 702 Talk Radio reported, citing the Airports Company South Africa (ACSA) as saying.
Irvin Khosa, of the local organising committee, blamed the problem on planes carrying heads of state which, he said, required special conditions which slowed the flow of other aircraft.
"When you transport heads of state, a free zone is required," he said.
"Two hundred and 20 flights came to Durban, especially charters. It was a case of force majeure."
TURN BACK
Five planes were forced to turn back to Johannesburg and Cape Town, while others landed after being delayed by several hours, leading to fans missing all or most of the mouth-watering clash between the two European football giants.
ACSA said passengers would not be reimbursed because the planes took off and landed at an airport and because only a small portion of the ticket price was paid to the company.
Stranded passengers, who spent thousands of rand on flight and match tickets, were outraged by the situation and some threatened to sue the airports company for their losses.
"We have done well up to now but today is a disgrace," one outraged fan told the radio station.
"The fact that one of our airports does not even know what its capacity is, is quite pathetic," said another.
Rich Mkhondo, spokesman for the World Cup local organising committee, told Reuters there was nothing the organisers could do about the incident now.
"Unfortunately, these kind of things happen. We will be meeting with ACSA later today to make sure this doesn't happen again during the final," he said.
FIFA general secretary Jerome Valcke denied reports that those who missed the game would be entitled to compensation.
"There will be no indemnity, this is not true," he said. "It's not our responsibility. What happened at the airport is an air traffic control problem. We had commercial partners and executive committee members who could not land in Durban."
Netherlands face Spain in the World Cup final at Soccer City in Johannesburg on Sunday.
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