Hapoel may have had more chances and possession on the night but they find themselves bottom of Group G on goal difference, level on three points with FC Lugano and FC Viktoria Plzen.
So qualification hopes hang in the balance, with trips Bucharest and Switzerland to follow before they conclude the group phase against Plzen at the Turner Stadium.
Maccabi Tel Aviv were brushed aside 4-0 by Astana in Group A. A first-half double from Patrick Twumasi plus two more from Junior Kabananga in the second half saw a sharper Astana team run out worthy winners.
Maccabi remain bottom of the group with no wins in three matches. They host Astana on November 2.