Leading 2-1 from the home leg, a superb 20-yard strike from Mitja Viler after 15 minutes eliminated the Israeli champions after an enthralling battle in Slovenia on Tuesday night.
With the advantage, Maribor sat back and Beer Sheva only threatened in the final 15 minutes with goalkeeper Jasmin Handanovic making a superb reflex save in the 89th minute to keep out a Tony Nwakaeme header.
Hapoel manager Barak Bakhar said: "We missed a huge opportunity. We were the better team over the two games but we didn't take our chances at home."
Hapoel go into the Europa League Group Stage draw where they will likely be joined by Maccabi Tel Aviv who lead 1-0 from the away leg against Altach.
