Chris Sutton thought he had put the Scots into the knock-out stages for the first time in the competition's new format when he cancelled out Juninho's second-half strike.
Celtic had already come back from a goal down when John Hartson levelled Giovane Elber's early header.
But with six minutes remaining, Swiss referee Urs Meier somewhat harshly penalised Bobo Balde for handball in the area as he jumped in a challenge with Peguy Luyindula. Juninho coolly converted the spot-kick.
The referee and his assistants needed to be escorted off the pitch as the Celtic management team and Henrik Larsson, who had to endure more heartache in the stadium after breaking his leg here in 1999, tried to challenge them.
It was a cruel finale to an action-packed Group A campaign as Lyon went through and left the Glasgow giants with the scant consolation of a UEFA Cup place.
Manager Martin O'Neill had promised to go on the attack despite needing only a draw to go through, but they were under intense pressure from the very first minute.
Liam Miller needlessly gave the ball away to Luyindula, who fed Elber. Stanislav Varga slipped at the worst possible moment and the Brazilian hit a powerful low shot which Magnus Hedman pushed away.
Sidney Govou then had the visitors in all kinds of trouble and when the ball broke to Anthony Reveillere, he fired just over from just outside the box.
It was no surprise when Celtic went behind in the sixth minute.
Juninho's free-kick came back off the crossbar and into the path of Elber to head into the empty net Moments later only a timely intervention from Johan Mjallby prevented the former Bayern Munich star from adding to his tally. But Lyon's bold four-pronged attack left them short at the back, and Celtic almost got back level on 16 minutes.
Larsson and Miller combined to feed Hartson in the box, but even though his shot was not on target, the Swede was close to getting a vital touch.
Sutton uncharacteristically gave the ball away on the edge of his box in the 18th minute and he was relieved to see Elber whistle a shot over the crossbar. Celtic bravely hauled themselves level on 24 minutes. Sutton headed Stilian Petrov's long ball into the path of Larsson and his shot was pushed out by Gregory Coupet, but fortunately for the visitors it dropped to Hartson to fire home.
But Celtic were still in disarray at the back and needed a fine save from Hedman to deny Luyindula Celtic felt they should have had a penalty on 32 minutes. Sutton went down in the box under the challenge of Jeremy Berthod, after being played through by Larsson, but the referee waved play on.
On-loan Michael Gray was being given a torrid time by Govou and the Lyon winger showed him a clean pair of heels, but then wildly lashed his shot over the bar with just Hedman to beat.
At the other end, Coupet failed to hold Miller's innocent-looking effort, but managed to jump on the ball as it rolled towards goal.
After the restart, the referee awarded Lyon a corner after Govou appeared to head wide, before Celtic fell behind again in the 53rd minute.
Juninho picked up the lose ball 35 yards out, strode forward and fired an audacious strike past Hedman Elber then blazed over after being put through by Luyindula and Claudio Cacapa was inches away from killing off the tie in the 64th minute when his header flew just past the angle from a corner. But against the run of play, Celtic fought their way back level again in the 75th minute when the ball broke to Sutton inside the box and he coolly slid it past Coupet.
O'Neill responded immediately by taking off the goal hero, who had picked up an injury, and bringing on an extra defender in John Kennedy.
But just when it looked Celtic had done enough, the referee awarded Lyon a penalty with six minutes remaining for what looked the slightest of touches from Balde's leading arm, and Juninho sent Hedman the wrong way.
LYON: Coupet, Edmilson, Berthod (Carriere 76), Reveillere, Cacapa, Diarra, Juninho (Muller 89), Malouda, Govou, Luyindula, Elber (Dhorasoo 87).
CELTIC: Hedman, Varga, Mjallby, Balde, Gray (Wallace 68), Lennon, Miller, Petrov, Sutton (Kennedy 80), Hartson (Sylla 68), Larsson.
Referee: Urs Meier (Switzerland).