Trailing Romanian side Cluj 1-0 from the away leg, Maccabi drew level on aggregate when recent signing Nick Blackman fired home 14 minutes into the second leg.
However, Maccabi's joy was shortlived as Cluj scored a crucial away goal from the penalty spot, with Culio converting just five minutes later.
And the Netanya Municipal Stadium was stunned into silence three minutes before half-time when Rondon scored Cluj's second of the night, to make it 3-1 on aggregate, meaning Maccabi would now have to score three more times to progress.
Substitute Cohen made it 2-2 on the night, but the Israeli champions were unable to muster any more goals to leave Cluj celebrating a money-spinning tie against Celtic.
Maccabi now drop into the Europa League, alongside the likes of Manchester United and Arsenal, where they will face Suduva.
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