The American, not included in many pre-race predictions, won in 1:49:48 from Dutchman Ferry Weertman who out-touched Greek defending champion Spyridon Gianniotis for the podium placings.
"It was not the result I was looking for. I felt good through the middle stages of the race but that last bit again I really need to continue to work on," Radford said.
"I guess now I have to quickly move on. I have a year to focus on the next qualifying race and I need to have a better showing than that to put my hand up for the Olympics.
"In the guys' field it is so stacked and on any given day anyone can get up it is that close."
Radford has one further chance of Olympic nomination at the second qualifying event in Portugal next May where a further nine places are available.
New Zealand's Charlotte Webby is in action tomorrow in the women's 10km race among 61 starters including London Olympic champion Eva Risztov (Hungary), defending world champion Poliana Okimoto (Brazil), the Pan Pacific winner Haley Anderson (USA) and World Cup leader Ana Marcela Cunha (Brazil).
The rest of the New Zealand team are at their staging camp in Barcelona with the pool competition to start on 2 August.