Skelton and Scott Brash finished equal fifth and Ben Maher ranked equal ninth as they failed to repeat the success that saw them take team gold – the first for 60 years – two days earlier with Peter Charles.
A fourth clear round of the competition for 54-year-old Skelton on Big Star in final round A was not enough to clinch a medal as he knocked down one pole in round B to pick up four penalty points.
Brash, riding Hello Sanctos, produced identical performances to Skelton and they finished equal fifth with Alberto Michan of Mexico.
Fellow Brit Ben Maher on Triple X III picked up four jumping penalties in each round of the final to position him ninth overall.
After missing out on the medal positions, Skelton revealed the team had anticipated taking home more silverware.
“Everyone thought it was going well, I did too, but I just touched the pole at the wrong time and that was it,” he said.
“I feel sorry for the people that came. We expected to win and it wasn't to be. But we got one gold, we would have settled for that before we came."
But Brash added that their Olympic experience has been an incomparable and unforgettable one.
“It has been amazing, the crowd have been amazing, and I am just disappointed for letting them down. I wanted to give them something to cheer about,” he said.
"I am just a bit gutted really. Once we go away from here, we will never get a feeling like this again."
The jumping individual gold medal was claimed by Steve Guerdat of Switzerland, who produced two faultless rounds on Nino des Buissonnets.
Meanwhile a jump-off determined the silver medal for the Netherland’s Gerco Schroder on Eurocommerce London and the bronze for Cian O’Connor of Ireland on Blue Lloyd 12.