Hearts were beaten 2-0 by Copenhagen at the Parken Stadium this evening.
Two second half strikes were enough to down Hearts in the Danish capital, Amin Chiakha finishing from close range before Kevin Diks smashed low into the bottom corner from the spot with twenty to play.
Neil Critchley's men will decide their qualification fate next Thursday when Moldovan side Petrocub come to Tynecastle.
The Danes enjoyed the lion's share of possession in the opening stanza, but rarely troubled Craig Gordon's goal - an offside header from Gabriel Pereira flashed high and wide over the crossbar before the Scotland international stuck a leg out to turn Robert's ball across the face of goal away from danger.
Hearts did well to survive a scare after 26 minutes as Viktor Claesson's go at goal was turned onto the woodwork by James Penrice as the Jambos scrambled to beat Copenhagen back.
Copenhagen maintained their dominance of the ball throughout the first 45, but parsimony in front of goal, combined with a solid defensive showing from Hearts, restricted any real chances of note as both sides went in at the break all square.
HT: Copenhagen 0-0 Heart of Midlothian
The Jambos' rear-guard was eventually breached within minutes of the restart as the ball fell kindly to Amin Chiakha within a goalmouth scamble - allowing the Algerian to dispatch a low drive past Gordon.
Hearts began to enjoy some more success with the ball thereafter. A Cammy Devlin effort from the edge of the box deflected into the path of Blair Spittal at the front post, with his flick on narrowly going over the bar.
Gordon was kept on his toes, as Copenhagen eventually worked the ball towards William Clem on the edge of the box; his ranged effort was struck low with the 'keeper forced down quickly to halt.
The Danes doubled their lead after 76 minutes as Kevin Diks converted from the spot; Craig Gordon penalised for an apparent foul.
There was to be no further action, with all to play for against Petrocub next week.
Copenhagen: Trott, Diks, Pereira, Hatzidiakos, Claesson © (Cornelius 87'), Elyounoussi, Lopez, Robert (Froholdt 80'), Chiakha (Mattsson 87'), Delaney, Clem (Lerager 80')
Subs: Sander, Runarsson, Garananga, Mattsson, Larsson, Lerager, Huescas, Cornelius, Froholdt, Goscholeishvili, Meling, Højer
Hearts: Gordon, Kent (Forrester 34'), Oyegoke, Shankland ©, Devlin, Rowles, Spittal, Forrest (Oda 72'), Boateng, Penrice, Vargas (Wilson 72')
Subs: Clark, Grant, McKay, Oda, Dhanda, Wilson, Tait, Boyce, Forrester, Sandilands, Salazar
