The voting was completed late in regular season by managers and coaches. The only stipulation was the managers and coaches could not vote for their own players.
Rendon was one of three finalists at third base in the National League. He lost out to Nolan Arenado of the Rockies.
Soto, who was joined by the Padres' Hunter Renfroe as a left field finalist, lost out to the Diamondbacks' David Peralta.
It appeared that Robles had the best chance of winning a Gold Glove for his work in center field, leading major league center fielders with 22 Defensive Runs Saved. But Robles was beat out by Lorenzo Cain of the Brewers for the Gold Glove.
During the postseason, Nationals manager Davey Martinez said he thought Robles and Soto and a good shot at winning the awards.
The last Nationals player to win a Gold Glove was first baseman Adam LaRoche in 2012. Ryan Zimmerman won a Gold Glove at third base in 2009.