City's Bernardo Silva and Mateo Kovacic both misfired in the shootout to put Madrid in the driving seat
Gomez Noya, the only triathlete to win five world titles, was among the favourites to clinch gold at this year's Olympics in Rio after claiming silver in London in 2012.
"Unfortunately this has forced me to pull out of competing in Rio. I need to be realistic, there is no time to prepare and to be fit on the start line of the games," Gomez Noya said on its Twitter account.
Gomez Noya recently won his most prestigious sports award, the Princess of Asturias prize, for his "brilliant achievements".