Livingston saw their hopes of salvaging their UEFA Cup dream crumble at Almondvale - despite a battling display against Sturm Graz.
The West Lothian side headed into the clash trailing 5-2 from the first clash in Austria.
Barry Wilson grabbed a brace and Davide Xausa and Marvin Andrews both netted for the home side in the return leg 4-3 victory but that was matched by a double from Imre Szabics and a goal from David Mujiri to give the Austrians an 8-6 aggregate win.
For an agonising eight minutes in the first leg in Austria it looked certain Livingston's European dream would end almost before it began.
That devastating spell at the Arnold Schwarzenegger Stadium allowed Graz to increase their lead to five goals and, as the game approached the final whistle, there seemed to be no way back for the Scottish Premier League side.
But two late goals - courtesy of Rolando Zarate and Stuart Lovell - gave the West Lothian side a glimmer of hope that they could progress to the second round.
Sturm Graz interim coach Franco Foda had yet to lose a game since taking over from Ivica Osim heading into the tie and the small travelling support of around 100 people indicated that most of the Graz fans believed the hard work had already been done.
Livingston`s Francisco Quino tried his luck within 30 seconds of the kick-off with an opportunist drive from 18 yards - but the ball fell wide of the post.
David Xausa and Barry Wilson then set up David Bingham in front of goal but, before he could connect, goalkeeper Daniel Hoffman had pounced off his line to deny the Livingston player.
The home side threatened again after 17 minutes when Gary Bollan's long free-kick found Bingham in the box - he nodded onto Xausa but his header was held by Hoffman.
Sturm Graz were unlucky not to take the lead two minutes later when Imre Szabics unleashed a shot from just inside the area that Javier Sanchez Broto did well to block.
Livingston's luck took a turn for the better when they were handed a penalty kick on the half hour mark when Wilson was felled in the box by Gunther Neukirchner.
Wilson stepped up to take the spot-kick himself and he threw the Scots a lifeline by sending Hoffman the wrong way from 12 yards to give the West Lothian side the lead.
The Livingston player attempted to retrieve the ball from the net - knocking over Hoffman in the process - and that was followed by a claim from Strafner that he had been on the end of a challenge from Quino but he was ignored by the referee.
But Livingston suffered a blow a minute before the break when Sturm Graz levelled. David Mujiri provided the cross for Szabics to nod past Broto from just a few yards out.
Within two minutes of the restart Mujiri handed Sturm Graz the lead when he took the ball past Oscar Rubio before bulleting home from the edge of the 18-yard box.
Xausa had the chance to pull Livingston level again a couple of minutes later with a free-kick just outside the area - but he sent the ball well over and Wilson saw a shot blocked by the keeper seconds later.
Sturm Graz went 3-1 up after 53 minutes when Mujiri released Szabics, who took the ball round Broto and Rubio before tapping home from close range.
Unperturbed, Livingston netted a minute later in a desperate attempt to claw themselves back into the game. David McNamee's cross was met by Xausa whose volley left Hoffmann with no chance.
Marvin Andrews came close when he met Wilson's corner only to nod just over the bar, while at the other end Neukirchner unleashed a shot across the face of goal but the ball fell just wide.
Livingston's persistence earned them another goal after 78 minutes when Bingham played the ball into the path of Andrews, who produced a looping header from eight yards to send the ball over the line.
The West Lothian side had the ball in the back of the net again when Bingham and rammed home from close range - but the goal was disallowed for offside.
Bingham appeared to have the ball over the line again when he hit the underside of the bar in injury time but the referee ordered play to continue.
But just seconds later, Livingston grabbed another goal when Wilson crashed the ball home from 25 yards to at least make sure of a plucky win on the night, even though their UEFA Cup campaign was over.
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