Swindon Primary Schools battled bravely against a strong Bristol side, but slipped to their second Cotswold League defeat.
They survived an early siege but, despite playing five in midfield, found their opponents difficult to break down and lost 3-0.
The deadlock was broken as Bristol's Horgan slipped the ball under goalkeeper Jack Sansum.
Swindon made changes at the break and, for the opening 15 minutes, enjoyed their best spell.
But Bristol's defence held firm, won a corner and a superbly delivered cross found Jones, who rose unmarked to head in off the underside of the bar.
Swindon conceded a third with less than five minutes remaining.
A speculative long ball was chased by Barnes and, although Sansum blocked his first effort, he squeezed home the rebound.
Now Swindon travel to Cotswold League champions Gloucester, knowing that anything less than a win will probably end their hopes of winning the league.
Swindon: Jack Sansum, Henry Finnegan, Sam Munton, Kristopher Redford, Ben Valentine, Connor Thompson, Stephen Bray, Nathan Hawkins, Josh Parsons, Ross Clifford, Josh Skeates. Subs: Jack Savage.
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