Motherwell boss Stuart McCall claimed his side were too soft against a resolute Stjarnan.
Motherwell led the tie on three separate occasions over the two legs, but still lost to the Icelanders with a winning goal deep into Extra Time in the Samsung völlurinn.
It was a sickening blow for the Steelmen; particularly given three of the five goals conceded over both legs were from the penalty spot.
The Fir Parkers had made a great start when Stevie Hammell headed home a well-worked corner during the first half.
But Ólafur Karl Finsen leveled things from the spot, again, before Lionel Ainsworth’s volley looked to have won it.
However, sub Rold Toft took the tie to extra time with a later leveler before Atli Johannssen’s long-range effort sealed it for the hosts with just minutes.
A downbeat McCall said: “This isn’t the time for lambasting people. To have been 2-0 up at Fir Park, then 1-0 and 2-1 up here in Iceland should have been enough.
“But we haven’t been strong enough to keep the lead. We had chances to kill them off but didn’t take them.
“Instead, we were soft right through and let them back into it.
“The second equaliser was the sore one – we should’ve been stronger defensively at that one.”