Two goals in four first-half minutes left Villa with a mountain to climb and despite riding their luck in the latter stages, the plucky Slovakian outfit held on to ensure their group stage programme ended with the high of one victory from their four games.
Having won both of their opening group games, Villa boss Martin O'Neill took the opportunity to rest a raft of first-team regulars after making eight changes to the side that started their last Premier League game.
There was a rare appearance for Marlon Harewood in attack, while Brad Guzan started in goal and 17-year-old academy striker Nathan Delfouneso was handed his first start.
Villa started brighter than the cold Midlands evening and forced a succession of corners before falling behind in surprise circumstances with 15 minutes on the clock.
Vladimir Leitner sent over a hopeful cross from the left which Zat Knight appeared ready to head away until he ducked at the last moment and the ball bounced past the helpless Guzan and into the far corner of the net.
It was to get worse for the home side just four minutes later when Zilina doubled the advantage.
Adauto was the architect of a superb flowing move as he ran at the heart of the Villa defence before playing in Peter Pekarik, whose cut-back was turned into the net with a neat side-footed finish from Peter Styvar.
The second goal seemed to wake Villa from their slumbers and Delfouneso marked his first start with an impressive volley to reduce the arrears.
Strike partner Harewood chested a long ball down to the teenager, who dispatched a thunderous first-time left-foot strike past the diving keeper on 28 minutes.
Villa started the second period at a high tempo, but it was Zilina who threatened first when the lively Adauto's 30-yard strike stung the palms of Guzan.
The home side continued to press with Harewood producing a couple of weak finishes from half-chances.
James Milner and Gareth Barry were thrown into the fray with 20 minutes remaining with the the result being an even greater domination of possession by Villa.
Craig Gardner almost bundled the ball home following a melee in the box on 75 minutes and Milner crashed the resultant loose ball the wrong side of the post.
Full-back Leitner was dismissed for pulling back substitute Gabriel Agbonlahor to earn his second caution of the night with 11 minutes remaining.
Luke Young failed to make a clean connection when arriving unmarked onto a deep cross as Villa turned the screw in a desperate attempt to get back on level terms.
Barry headed an Ashley Young cross over the bar in the closing minutes, before Gardner guided a header onto the post in stoppage time as Villa failed to find the equaliser their second-half dominance deserved.