Celtic's European hopes ended in frustrating fashion after substitute Ciro Immobile's late double denied them what would have been a creditable draw with Lazio.
Brendan Rodgers' side needed to win to preserve any hope of progression in the Champions League, or even the consolation of a Europa League spot. And while the Scottish Premiership side were resilient in Rome, they struggled to eke out chances.
Lazio endured an exasperating evening themselves but ultimately could rely on the quality of Immobile.
The Italy striker flashed a deflected Gustav Isaksen cross past Joe Hart in the 82nd minute, then capitalised on a Liam Scales misjudgement three minutes later to cut inside Cameron Carter-Vickers and roll in a second.
The win was enough to confirm Lazio's place in the last-16 after Atletico Madrid beat Feyenoord 3-1 in Rotterdam.
And it means Celtic's meeting with the Dutch in Glasgow in two weeks will be a dead rubber for both sides, as well as the Scottish champions' final continental game of this term.
After that, they will reflect on a frustrating campaign and one undermined by red cards and lapses of concentration.
Celtic avoided the former in Rome, but the latter were again in evidence, even if there was an admirable doughtiness about much of their play. Too often, promising scenarios floundered on the back of a slack pass or split second of indecision.
Their best moments came early in the second half. Kyogo Furuhashi skidded wide from the apex of the area before Yang Hyun-jun inexplicably headed away from goal in the hope of finding a team-mate when an attempt on target was on.
That was as good as it got, with even a late penalty award - and the chance of a slither of consolation - overturned.
Lazio, out of form and in a bad place domestically, were similarly sloppy for much of the game, but the Serie A side possess a menace in the final third that Celtic lack.
Felipe Anderson, Taty Castellanos, Isaksen and Luis Alberto all spurned fine chances before Immobile removed his jacket and showed them how to do it.
He was the difference and ensures Lazio's European adventure continues, while Celtic's draws to a close.
Lazio with Ciro Immobile in attack are a far better team than Lazio without him. The Italy international brought a gun to a knife fight
He scored at Celtic Park and he scored when the sides met here in 2019. But neither of those goals were quite as painful as Immobile's late efforts on this occasion.
Lazio weren't great. Celtic might have got a draw. They might even have found the win that would have extended their European campaign. But instead they were again left to rue a late lapse.
Rodgers' Champions League record is now played 23, won four with Celtic, who are winless in their last 14 in this competition, losing 11.
This season has now gone, but there's every chance they will be back next term. How do they find a way of being more competitive?
Celtic manager Brendan Rodgers: "In the last 20 minutes we looked like the team that could go on and get the result, but we gave away two poor goals.
"This group has gained more experience and shown they can compete in some games - but we need to add quality. That's the glaring thing that stands out."
Celtic host Feyenoord in their concluding Champions League game on 13 December (20:00 GMT), but first they travel to Perth to face St Johnstone on Sunday (12:00).