The Fir Park side have now gone
10 games in a row in continental competition without a win and have crashed out of Europe at the first time of asking in their last four campaigns. Yet they only have themselves to blame after blowing a two-goal lead in the first leg last week and twice losing the lead in Reykjavik
last night against the Icelandic side, the second, and ultimately fatal,
occasion to a dipping volley by Atli Johansson that might have been saved by Dan Twardzik.
However, Stuart McCall played down suggestions his players had been left red-faced by their part-time opponents.
"I'm disappointed to be out but it's not embarrassing. Everyone keeps going on about them being part time but they train every day and have lost one game in their last 16. But we should have won over the two ties and we haven't," said the Motherwell manager. "Missed chances, as well as poor defending, cost us and their winner was a speculative effort.
I spoke to the keeper afterwards and he said it moved a lot but he should have punched it against the crossbar."
It was a desperate loss against a team Motherwell should have beaten comfortably and it was a disastrous tie for their captain Keith Lasley who conceded three penalties in two games - all of them converted by Olafur Karl Finsen - missed an extra time sitter and was booked.
Goals from Steven Hammell and Lionel Ainsworth should have been enough, but they simply didn't know how to defend a lead.
"We were soft right through. We should have killed the game off at 2-1. We scored from a well-worked corner then shot ourselves in the foot with another penalty. And then we conceded a terrific second and I couldn't see how they were going to score but they carved right through us and it was a soft goal to lose. We had two or three really good chances in the first period of extra-time and if we got a third they would have needed two. I have no complaints over their penalty."
McCall picked the same team
as he had done last week and they started in the same positive manner by forcing a couple of corners within the first five minutes in Stjarnan's tiny, but sold-out Stjornuvollur stadium. But they were also given a quick indication of how dangerous the home side could be when Pablo Punyed's shot drifted wide.
However, the Scots stunned the home fans by taking an 11th-minute lead thanks to another corner. Ainsworth picked out the unmarked Hammell who bulleted a header into the top corner from 15 yards out, for hist first goal for the club since March 2012. It was the perfect start for the visitors and their 250-strong support.
But the home side were also winning their fair share of corners, with each of them appearing to be accompanied by a bizarre impromptu disco by the excitable home fans and they were certainly creeping into the game as the half progressed.
Stephen McManus almost got into trouble when he slipped on the artificial pitch while trying to cut out a cross and he was lucky Arnar Bjorgvinsson scuffed his shot right in front of goal. So it wasn't a huge surprise when the home side equalised in the 37th minute and once again it was down to a penalty conceded by Lasley - the third he'd given away in the tie.
He took an extra touch when trying to clear his lines and bundled Johansson over in the box. The Greek referee Athanasios Giachos took his time before pointing to the spot, with Motherwell's players insisting it was a harsh decision. Finsen easily converted the penalty to give the Icelanders the aggregate lead thanks to the two away goals the same player had scored in Scotland.
Simon Ramsden and Lasley both went close to regaining the initiative for the Scottish Premiership runners-up as collectively the visitors realised they would have to raise their game significantly if they were to progress.
Yet they almost lost another goal seven minutes into the second half, when Stephen McManus was weak in a challenge and it took a fine save from Twardzik to deny Arnar Bjorgvinsson.
Lasley almost redeemed himself when he attempted a clever chip after a corner was laid to him, but the backpeddling home goalkeeper Ingvar Jonsson got back in time.
The Lanarkshire side came even closer on the hour mark when the home defender Daniel Laxdal hit his own post as Motherwell started to take command again and they regained the lead in the 66th minute courtesy of some superb wing play by Josh Law. The summer signing, who hit two on his debut in the first leg, bolted down the left before delivering a peach of a cross to the back post which was turned in by a stretching Ainsworth on the volley.
But McCall's side failed to learn their lesson and conceded another soft goal with five minutes remaining. The substitute Rolf Toft was allowed far too much time and space in the box and he fired easily into the roof of the net with Motherwell's defence looking suspect again.
In extra time, Lasley had another chance to make amends when he had only Jonsson to beat, but took an age to shoot and his effort was charged down.
Then came the winner. Johannsson volleyed in with six minutes left with a 25 yard drive that swerved and dipped over Twardzik's head, to spark wild celebrations.