Trailing 1-0 from the opening match against the Azerbaijan club, the Dons' task was made all the more difficult by an early strike from Tural Bayramov.
Kady Borges and Abdellah Zoubir then added further goals to pile on the misery, with a stoppage-time penalty from Lewis Ferguson little more than a consolation as Aberdeen were beaten 4-1 on aggregate.
Missing key players in the shape of injured Andrew Considine, Ryan Hedges and Connor McLennan, the Dons were soon facing an uphill battle.
A throw on the left was worked into the box for Bayramov, who struck a sweet left-footed strike across Joe Lewis and into the far corner to put the visitors ahead after just eight minutes.
Aberdeen needed to respond quickly but could have been further behind had Abbas Huseynov's cross been turned in by Borges, who inexplicably missed his kick on the six-yard line.
The second came soon enough though, with Ross McCrorie's loose pass out from the back putting his side in trouble. Qarabag were on top of the Dons goal in no time and Borges stroked home Zoubir's pass with ease.
Indeed, Qarabag could have had a third two minutes before the interval as Ramil Sheydaev got between Declan Gallagher and Lewis, but could not lift the ball over the Dons goalkeeper.
Jonny Hayes finally tested visiting goalkeeper Shakhrudin Magomedaliyev from 18 yards after 62 minutes, and although his save was unorthodox, he was able to push the effort wide.
All hope was extinguished 10 minutes later when Zoubir found the net. It was all too simple as he was set clear through the middle, shifting the ball on to his left foot before sending a low drive past Lewis from 15 yards.
With the tie well won, Qarabag seemed to take their foot off the gas and Funso Ojo's 20-yard strike was not far away from giving the hosts a consolation, fizzing millimetres over the crossbar.
The Dons were handed some late relief from the penalty spot as Calvin Ramsay went down and Ferguson - after a brief delay while a pitch incursion was dealt with - fired home, but it was too little too late.