Celtic crashed out of Europe after a thumping 3-0 defeat by AC Milan in their Champions League Group H clash at Parkhead.
With Ajax beating Barcelona 2-1 at the Amsterdam Arena, the Scottish champions do not even have the safety net of the Europa League this season.
Brazilian star Kaka put the visitors ahead in the 13th minute when he headed a Valter Birsa corner past Hoops goalkeeper Fraser Forster.
Celtic defender Virgil van Dijk missed a sitter at the start of the second half when he blasted a shot straight at Milan goalkeeper Christian Abbiati, a minute before Rossoneri defender Cristian Zapata made it 2-0 from close range.
Mario Balotelli, in one of his more productive moods, scored a third with a drive on the hour mark to compound the misery of the home side who were made to pay for missing several chances.
Celtic remain bottom of the pool with three points from five games and their final fixture at the Nou Camp next month will be for pride only.
For what was built up into a do-or-die tie, Lennon was without suspended duo Scott Brown and Nir Biton and he brought in Mikael Lustig, Beram Kayal, James Forrest and Derk Boerrigter.
Joe Ledley, Darnell Fisher and Teemu Pukki dropped to the bench to be joined by Anthony Stokes who missed the Dons game with personal issues.
The Italian side arrived in the east end of Glasgow in some turmoil having won just three of their 13 Serie A matches this season and without a win in seven.
However, their star-studded line-up included Kaka, Balotelli and captain Riccardo Montolivo.
Lennon had warned against reading too much into the poor form of the Rossoneri - a warning which proved to be right.
The home side, captained by Georgios Samaras who was leading the line, had the first chance of the match in the second minute when a Charlie Mulgrew corner was met by Boerrigter but the Dutchman failed to connect properly.
However, the visitors hinted at danger early on when Balotelli drew a shot wide of the target.
Celtic had an even better chance in the ninth minute when Kayal found himself with the ball at his feet in front of goal following a shot from Mulgrew, but the Israeli midfielder hesitated, allowing Zapata to challenge before he skewed his drive wide.
The Hoops looked capable of getting the win they so badly needed but their fans were stunned into silence at Kaka's goal.
Unmarked at the six-yard box when Birsa's corner came over from the right, the former Real Madrid player had the easiest of tasks heading past Forster.
Celtic responded as expected but Milan remained potent.
In the 25th minute Boerrigter's header from a Forrest cross was blocked by red and black shirts moments before Milan broke up the park with purpose, Balotelli finishing the move by firing just over the bar.
A couple of minutes later, Kaka drove a powerful curling drive from 22 yards which beat Forster but just evaded the far post.
Kayal limped off to be replaced by Ledley just on the half-hour mark.
In the 36th minute, after Kris Commons was crowded out at the edge of the Milan penalty area, the ball broke kindly to Mulgrew but his left-footed shot was too weak to bother Abbiati.
Balotelli then had the ball in the net after breaking clear of the Hoops defence but the flag was up early for offside.
The game turned in a minute early in the second period.
In the 47th minute, when Mulgrew's free-kick was blocked by the wall he lobbed the ball into the box to find the unmarked van Dijk but the Dutchman blasted a volley straight at Abbiati.
A minute later the Hoops were two behind and on their way out of Europe.
Birsa's lofted corner from the right was met by substitute Antonio Nocerino, on for Ignazio Abate, and he steered the ball across goal to the back post where Zapata was in perfect position to knock it in from a yard out to deliver a hammer blow to the Hoops.
Celtic looked as if they had got themselves back into the game soon afterwards when Van Dijk headed in a Ledley cross but the offside flag was up.