Villa arrived in the Netherlands on a five-match winning streak across all competitions, but their momentum came to a sudden halt as the hosts produced one of the biggest upsets in their European history.
Evann Guessand gave Villa the perfect start after just four minutes, slotting home after goalkeeper Jari De Busser could only parry Jadon Sancho's cross into his path for his first goal for the club since joining in the summer. Sancho impressed early on, forcing a save from De Busser after a jinking run, while Buendia later created a chance for Guessand, who dallied on a through-ball and was denied by the keeper from close range.
Despite Villa's dominance, Go Ahead Eagles levelled just before half-time. The Villa defence failed to deal with a floated free-kick and Mathis Suray saw his shot take a huge deflection before looping into the top corner.
The Dutch side then completed a remarkable turnaround midway through the second half when captain Mats Deijl controlled a cross from Joris Kramer with his chest before poking past Emiliano Martínez from close range to make it 2-1.
Emery reacted by making several substitutions, bringing on Morgan Rogers, Donyell Malen and John McGinn in a bid to salvage the game. Rogers crashed a cross-shot against the woodwork and later curled an effort inches wide.
Villa were awarded a late penalty in the 77th minute after Dean James handled the ball in the area. However, Buendia's spot-kick flew over the bar amid swirling wind and rain, compounding Villa's frustration.
Speaking after the match, Emery defended his side's performance but admitted his disappointment at the result.
"Today was a match we were dominating, we were creating chances, and we scored the first goal. We conceded a few chances to them and they were clinical," Emery said.
"They competed very well, defending fantastic. We tried with the penalty we had, but we missed it, and we have to accept it. I'm positive, but today I'm feeling disappointed and a little frustrated."
The defeat ended Villa's winning run and denied them a first back-to-back set of away victories in major European competition since 2008. Go Ahead Eagles, meanwhile, celebrated their most famous night, moving level on points with Villa in the group stage standings.
Villa return to Premier League action on Sunday when they host Manchester City, where Emery will be hoping for an immediate response from his players after a night to forget in Europe.
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