Sweeny was part of a five-man breakaway that managed to hold off the peloton in Cistierna, with Jesús Herrada (Cofidis) prevailing ahead of Fred Wright (Bahrain-Victorious), Samuele Battistella (Astana Qazaqstan) and Jimmy Janssens (Alpecin-Deceuninck).
Herrada's victory on the 190-kilometre stage left Sweeny disappointed with his performance despite working hard on both the Puerto de San Glorio and undulating run-in to the finish.
The peloton's pursuit of the quintet seemed to stall once Australian Luke Plapp (Ineos) swung off the front of the main bunch, and that lull was enough for the breakaway to preserve their final margin of 29 seconds.
For Sweeny, a case of bad legs - one he attributed in part to the first rest day - came at the worst time as he looked to secure a maiden stage win at a Grand Tour.
"I didn’t feel great and I even doubted if I could survive the long climb," Sweeny said via Lotto-Soudal's website.
"That is why I did a lot of turns on the front: that way I could ride my own pace. Fortunately, I could hang on and afterwards, it was a big battle between us and the peloton. But we kept on working together really well, until the final kilometre or so when it became clear that the stage winner would be at the front.
"I started the sprint in a good position but pretty soon, I realised that I didn’t have the best of legs. I did everything I could today, but it still remains a big disappointment.
"With this type of finish and the good position I started the sprint in, a lot more could have been possible on a good day. But it is what it is. We keep on aiming for that stage victory with the whole team."
Sweeny's frustration was Herrada's elation at the finish line, as the Spaniard collapsed in tears after securing Cofidis' biggest victory of the season.
Remco Evenepoel (Quick-Step Alpha Vinyl), meanwhile, finished in the chasing pack to retain his 21-second advantage over Rudy Molard (Groupama-FDJ) in the overall standings.
La Vuelta continues tonight with a summit finish to Collau Fancuaya, the hard climb set to see a battle for the stage and red jersey as the top climbers again get the chance to make their mark on the Spanish Grand Tour. Watch from 9:05pm (AEST) via SBS On Demand, with the SBS broadcast starting at 10:30pm. WA viewers can watch from 8:20pm (AWST) on SBS VICELAND.
