The 39-year-old trailed home in a time of 27 minutes 20.39 seconds, nearly nine seconds behind winner Tariku Bekele in a race staged as an official Ethiopian Olympic trial.
"I was wondering if I can run, you know, just the top three, but it did not work," Gebreselassie told Reuters. "The last 400m it was not good for me."
Gebreselassie admitted his Olympic dream had died.
"That's over, yeah," he said. "No more."
Bekele finished in 27:11.70, just ahead of Leleisa Desisa Benti who will join him in London. The third spot in the Ethiopian team is being held open for world record holder Kenenisa Bekele who has been suffering from injury problems.
Gebrselassie had been hoping to travel to his fifth Olympics and was in confident mood after winning the Great Manchester Run last weekend. He won gold in the 10,000 metres in 1996 and 2000.
Santos Luguelin of the Dominican Republic set the second-best time of the year in the men's 400 metres.
The 18-year-old won in 44.45 seconds, a time only bettered by American Olympic champion LaShawn Merritt in 2012.