Maccabi Haifa crashed out of the Europa League after going down 3-0 at home to Schalke in their final match in Group J.
Needing a win to guarantee qualification into the round of 32, Yaniv Katan, the former West Ham striker, had a penalty saved with the Israelis trailing by a goal and their fate was settled with Steua Bucharest beat Larnaca 3-1 to pip them to second place.
Haifa got off to the worst possibly start when Jurica Buljat scored an own goal past keeper Bjoan Saranov after seven minutes.
Katan was denied by Timo Hildebrand from 12 yards with 17 minutes remaining and the Germans rubbed salt into Haifa's wounds with goals from Marica and Wiegel in the last six minutes.
Maccabi Tel Aviv earned a creditable 3-3 draw against Dynamo Kiev.
Atar, Vered and Dabbur registered for Maccabi who finished bottom of Group E on two points.
With all Israeli teams now out of Europe, Hapoel Tel Aviv conclude their campaign at home to Legia Warsaw in Group C tomorrow.