Neil Lennon's side looked on course to get the score draw they needed to accompany Barcelona through from Group G when Georgios Samaras' 32nd minute header cancelled out Ola John's early opener.
However they proved unable to hang on in the second half, Ezequiel Garay volleying home a superb winner with 19 minutes to play at the Stadium of Light.
The defender smashed home a knock-down from fellow centre-back Luisao to put the Portuguese back in front just seconds after team-mate Salvio had fluffed his lines in front of goal.
Celtic tried to conjure a late leveller as they aimed to enjoy another famous night in Lisbon, super-sub Tony Watt - a goalscorer in the stunning victory over Barcelona a fortnight ago - going close in injury time with a right-footed drive that Gary Hooper was fractions away from turning in.
In the end, though, the Scottish champions suffered yet another loss on their travels in Europe, meaning they will have to better Benfica's result in Spain when they host Spartak Moscow in the final round of matches.
Despite knowing destiny was in their hands at the Stadium of Light after Barcelona's 3-0 win in Russia earlier, Celtic never really settled; a shaky start saw them fall behind after just seven minutes, John thrashing a right-footed drive beyond Fraser Forster after a deflected cross had fallen in his path.
Yet by half time their hopes had been rekindled thanks to Samaras, the Greek forward allowed to nod in Charlie Mulgrew's corner from no more than three yards out.
The loss of Mulgrew to illness at the break did not help their cause, though even more concerning was the second-half booking picked up by Victor Wanyama which means he will now be suspended for the Spartak match.
Benfica made sure that fixture would not be a dead rubber by getting their noses back in front, Garay's accomplished finish giving the otherwise outstanding Forster no chance.
Indeed, only a combination of the woodwork and the goalkeeper denied the hosts from increasing their lead in a frantic finish, Oscar Cardozo seeing a free-kick tipped onto the bar before Forster then denied the forward with a stunning reflex save.
Celtic had their opportunities too, but once Beram Kayal blasted a volley from 20 yards over the bar in injury time they knew it was not to be. Lennon's troops are already certain of a place in the Europa League next year, but that would be of little consolation after their efforts so far this season.