Barry crashed out of the Champions' League at Jenner Park when only pride was at stake following their 5-0 humiliation in Latvia last week.
The Welsh title holders could not even take advantage of a gilt-edged second-half chance to snatch an unlikely draw.
Striker Jamie Moralee blasted a 59th-minute penalty high over the bar just seven minutes after the Latvian champions had made it 6-0 on aggregate.
Impressive front man Maris Verpakovskis out-paced Gary Lloyd down the left and his accurate cross was side-footed home from 10 yards by Vladimirs Kolesnicenko.
Manager Kenny Brown made four changes to the starting line-up, including dropping himself to the bench, with former West Ham United and Manchester City star Ian Bishop in midfield.
Bishop's influence was minimal and his sole telling contribution was a through ball which led to Moralee being brought down Viktors Morazs.
Barry had enough possession, but failed to test giant goalkeeper Andrejs Pavlous, who used the many misplaced crosses for practice.
Skonto dominated midfield with Olegs Blagonadezdins, Zurabs Mentesasvili and Mants Samusevs all prominent as they held the upper hand.
Far happier
The talk of the first-half was a judgement by Icelandic referee Gylfi Thor Orrason that Kolesnicenko had dived when he went down under a challenge by Barry goalkeeper Simon Rayner.
It appeared to be a clear-cut penalty only for the striker to suffer further indignity when he received a yellow card for the offence.
After the game, Barry manager Brown said he was determined to see Barry in the competition next season.
"I'm disappointed in the result, but I was far happier with this display than the match in Latvia," he said.
"Now I'm determined to see Barry win the League of Wales agains and return to the Champions League again."
Barry Town: Rayner, Jarman, Lloyd, Kennedy, Phillips, Toomey, French, Moralee, Cotterrall, Pratt, Bishop. Subs: Dean Lee, Ramasut, Jenkins, Burke, Brown, York.
Skonto Riga: Pavlovs, Isakovs, Zemlinskis, Samusiovas, Dedura, Blagonadezdins, Morozs, Menteshashvili, Miholaps, Kolesnicenko, Verpakovskis. Subs: Dorosevs, Zakresevskis, Jelisejevs, Korgalidze, Ksanavicius, Kalnins, Rizevskis.
Referee: G Orrason (Iceland).