Trailing 4-1 from the first game in the Pepsi Arena last week, a difficult task for the Hoops became impossible when Michal Zyro notched in the 36th minute to quell any notions of a famous fightback.
The Scottish champions were booed off at the interval and when Michal Kucharczyk added a second on the hour mark the atmosphere threatened to turn ugly for a while with the home side and fans ultimately happy to escape without further punishment.
This crucial tie was Ronny Deila's first big test as Parkhead boss since taking over from Neil Lennon and he came up well short.
Celtic drop into the Europa League play-off which is unlikely to stimulate their fans and while the loss of Champions League money - £20million is a familiar figure - will not debilitate the Parkhead club, there may be ramifications.
Few will be surprised if 'keeper Fraser Forster leaves for pastures new but others such as defenders Virgil van Dijk and Adam Matthews may feel the time is now right to move on.
Moreover, without the lure of European football's elite club competition, Deila may find it difficult to attract the quality of player supporters want to see.
It was crystal clear, over the two legs against Legia, that the former Stromsgodset manager's squad needs bolstering.
Without defender Efe Ambrose - who was sent off in Poland last week - Deila brought in left-back Emilio Izaguirre, midfielder Nir Biton and striker Anthony Stokes with Teemu Pukki and Jo Inge Berget dropping to the bench.
Winger James Forrest started among the substitutes after recovering from a groin injury and he watched his team mates, almost inevitably, push forward from the start looking to get a foothold in the tie.
The home of Scottish rugby - being used again as Celtic Park remains out of commission after being used in the 2014 Commonwealth Games - was far from full and understandably could not replicate the atmosphere of a European night in the east end of Glasgow.
Nevertheless, there was an optimism emanating from the Hoops support as they urged their team forward.
But Legia looked potent going forward and in the 10th minute skipper Ivica Vrdoljak, who missed two penalties in the first game, had a speculative effort from 20 yards which required attention from Forster, seconds before his counterpart at the other end, Dusan Kuciak, did well to smother a Matthews cut-back.
The visitors had certainly not travelled to Edinburgh just to defend which led to an open encounter with both teams swapping shots on goal while neither were particularly diligent in possession.
In the 33rd minute Matthews drove down the right and into the Legia penalty area again but failed to find a team mate with his pass, to the frustration of the home supporters and Stokes in particular.
Three minutes later, it was all over for Celtic.
There seemed no immediate danger when Kucharczyk sent Zyro through against just Izaguirre but he left the Honduran in his wake, drawing Forster and slipping the ball into the corner of the net.
The Glasgow side tried to rally after the break but to no avail.
Stokes forced a good save from Kuciak with a curling shot from 20 yards in the 56th minute before Kris Commons went close with an effort which just escaped the far post.
Striker Leigh Griffiths replaced defender Mikael Lustig which required a reshuffle, captain Charlie Mulgrew dropping back to defence but the Hoops were disjointed and dispirited, all too easily allowing Kucharczyk to sneak into the box, take possession of a Zyro flick and round Forster before knocking in from an angle.
The fans began to turn their ire on chief executive Peter Lawwell as they contemplated the loss of more goals.
Pukki replaced Commons, and Forrest came on for Stokes but there was still no way through for Celtic, the noise of the final whistle immediately drowned out by more frustrated boos from those home fans who had stayed to the end, while a healthy travelling support celebrated.
Source : PA
Source: PA