Lyon coach Claude Puel has only held on to his job thanks to the European exploits of his team, which had already qualified for the last 16 knockout phase of the competition before Tuesday's home encounter.
But the look on club president Jean-Michel Aulas's face when Eran Zahavi gave Hapoel a 2-1 lead in the 69th minute with a superbly-taken overhead kick suggested Puel's troubles may not be over yet.
Lyon consequently slipped to second place in the group at the expense of Schalke, who stunned Benfica 2-1 in Lisbon, though that result was not enough to see the Israeli side leapfrog them into third place and a spot in the Europa League.
Puel, who guided Lyon to the semi-finals last season, bemoaned his side lacking a clinical edge both in their finishing and defending.
"I am disappointed but at the end of the day there will be no consequences from such a result...we just have to focus on our next league match against Toulouse," said Puel.
Hapoel's coach Eli Gutman was left both proud, and bitter.
"We played a superb match, and missed out on qualifying for Europa because of a few minutes when we lacked concentration.
"I'm very proud of my players, but it's a bitter result for us."
Lyon signalled their intentions from the outset and Bafetembi Gomis headed home in the 14th minute, only to be ruled off-side.
However Hapoel were not in France to make up the numbers, and the lively Toto Tamuz pounced on a loose ball and let loose a cannon of a shot which Lyon keeper Hugo Lloris did well to parry.
Moments later Lyon spurned a great chance to open the scoring when Gomis unselfishly squared for Jean II Makoun while under pressure, however Vincent Enyeama produced a fine save to stop the Cameroonian midfielder's shot.
Gomis then unleashed a 25-yard drive which Enyeama did well to parry, and a minute later the keeper was glad to see Makoun miss his second chance of the half when he sent his shot wide.
Sensing a chance to overtake Benfica and finish third place in the group, Hapoel kept pressing after the interval but it was Lyon who broke the deadlock.
Confusion reigned in the Israeli defence and Argentine striker Lisandro pounced on Enyeama's poor clearance when the Nigerian keeper panicked under pressure just after the hour mark.
Lyon's joy was short-lived, however. First-half substitute Ben Sahar found space on the left and, despite pressure from Cris, looked up and picked his spot before placing a left-footed shot beyond the reach of Lloris.
Zahavi then stunned the Stade Gerland into silence when he turned his back to goal and sent Toama's inch-perfect cross from the left past Lloris.
Five minutes from time Enyeama made amends for his earlier error with a superb parry of Lisandro's low volley from close range.
However, under increasing pressure from Lyon the Nigerian was well beaten when Alexandre Lacazette ran on to Lisandro's neat backheel to grab the equaliser with a low, angled shot two minutes from regulation time.
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