A night that promised so much for Sligo Rovers ended in complete devastation as they lacked the belief to put mediocre opponents to the sword.
They imploded in the second-half and have kissed goodbye to an additional €300,000 and a second round date with Norwegian giants Rosenborg next week.
Steven Lennon, the former Dundalk player, scored both of the Icelandic side’s goals to go with his late winner in the first-leg.
But while his first here - just seconds before half-time - was a considerable blow, it really shouldn’t have rocked the hosts as much as it did.
Liam Buckley’s men had played well up to that point and had a swagger about them that suggested this was their tie for the taking.
Yes, they squandered scoring chances but you sensed it would come right even at 2-0 down, but they were all at sea throughout the second-half and unravelled spectacularly.
Johnny Kenny’s late goal from the penalty spot was consolation and no more and the home side’s frustrations were summed up at the death when players on both sides squarred up.
Needing to score, Rovers’ attacking intent was evident from the outset and they completely dominated the opening half until that moment of madness just before the break that saw FH stretch their aggregate lead.
The hosts bossed all aspects of the half before that and got tremendous joy from balls over the top of the Icelandic defence. Centre-back Gudmundur Kristjansson was targeted repeatedly and endured a torrid time.
Petur Vidarsson’s presence alone put David Cawley off close to goal after a fine move initiated by Jordan Gibson and involving Romeo Parkes, who should then have scored himself midway through the half.
The former Jamaican international swept a ball just wide of Gunnar Nielsen’s post from a Walter Figueira ball and at that point it was a case of when, not if, Sligo Rovers would score. Parkes then flashed a header wide but the connection wasn’t clean.
Jonatan Ingi Jonsson was FH’s most dangerous player but team-mates struggled to find the diminutive wide man but he and Lennon looked capable of packing a punch on the visitor's rare surges forward.
But considering the height in their side, they posed a threat from set pieces and when Lewis Banks conceded a soft free near the corner flag a minute before half-time, FH capitalised in ruthless fashion.
Vidarsson’s ball into the box wasn’t cleared and lurking Lennon smashed home from eight yards to silence the 400 fans in the Showgrounds.
If that was entirely against the run of play, what unfolded next was entirely of Rovers own making. Just three minutes into the second-half and Regan Donelon tugged at Jonsson in the box to concede a needless penalty which Lennon blasted home.
It was hard to fathom how this got away from Buckley’s side, but ultimately they lacked a clinical edge in attack. Parkes would later skim another header wide and it summed up their struggles in failing to bury a team that was there for the taking.
New signings Adam McDonnell and Seamas Keogh added bite and a sense of urgency to a struggling side that had lost its shape and sense of purpose. So too did hot-shot striker Kenny who won and scored a penalty with six minutes to go.
And the teenager nearly stabbed home a second on the line at the death, but was snuffed out. Either way, it was all too little too late for the hosts who blew a golden opportunity to advance and swell the bank balance.
SLIGO ROVERS : McNicholas 6; Banks 6, Buckley 6, Blaney 6, Donelon 5 (Kane 71, 5); Cawley 5 (Horgan 71, 5), Morahan 5 (McDonnell 80, 5); Figueira 6, Gibson 6 (Keogh 79, 5), De Vries 5 (Kenny 59, 6), Parkes 6.
FH HAFNARFJORDUR: Nielsen 6; Vidarsson 5, Thorisson 6, Kristjansson 5, Gunnarsson 6; Dimitrijevic 5 (Gudlaugsson 73, 5), Sverrisson 5 (Robertsson 82, 5), Jonsson 6; Lennon 7 (Hreidarsson 90, 4), Vilhjalmsson 6, Jonsson 6 (Arnarsson 90, 4).
Referee: Luis Teixeira (Portugal)