Substitute Alexandre Lacazette salvaged a point for Lyon with a last-gasp goal but the home players were booed off their Gerland pitch by an angry crowd.
Goalkeeper Lloris was forced to make several spectacular saves as centre-backs Cris and Pape Diakhate delivered a dismal performance.
Both were caught out in the 63rd minute when Shay Abutbul's defence-splitting pass found Ben Sahar, who scored a well-deserved equaliser a minute after Lisandro Lopez opened the scoring for the home side.
Eran Zahavi put Hapoel ahead with a bicycle kick in the 69th minute.
"We enjoyed possession, we took risks and eventually we conceded a goal on a counter-attack," said full back Aly Cissokho. "We lacked coordination."
Lyon, who had already qualified after winning their opening three Group B games, have conceded nine goals in their last three outings.
They finished second in Group B on 10 points, three adrift of Schalke 04, and will take on a team who finished top of their group in February.
"It is true that we have been having defensive problems for a while," Cissokho said. "Nine goals in our last three European matches, it's a lot for a team that has qualified."
Lyon, who reached the semi-finals last season and will be playing in the knockout phase for the eighth consecutive year, now have two months to get their act together.
"We still make too many mistakes and we need to correct this," midfielder Maxime Gonalons added.
Coach Claude Puel, however, refused to panic.
"We lacked aggressiveness but there were no consequences," he told French TV Canal Plus. "We worked hard, we have an ambitious squad. You (the media) can bury us, we will show our worth in 2011."
