The east Belfast club had held the Icelandic league leaders to an impressive 0-0 draw last week.
But the Glens failed to put in the same defensive performance in the second leg on Thursday night, losing out on about £100,000 that would have eased the cash-strapped club's financial woes.
Goals from Gary Martin and Jonas Saevarsson saw Reykjavik through to the second qualifying stage and denied Glentoran a Europa League clash with Belgian side Standard Liege.
Elsewhere, Crusaders were demolished 7-2 by Norwegian side Rosenborg, and Drogheda United were beat 2-0 by Malmo.
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