On a night of high drama in Poland, the visitors took the lead through Callum McGregor in the seventh minute but proceeded to collapse, losing both a brace to the Legia striker Miroslav Radovic before the break and then a player, Efe Ambrose, to a red card a minute shy of the interval, for a last-man challenge on Michal Kucharczyk.
In the second-half, Celtic were spared further ignominy when the Legia captain Ivica Vrdoljak missed the target with a penalty, after Charlie Mulgrew was adjudged to have fouled Ondrej Duda inside the box but, in the 84th minute, Michal Zyro headed in No.3 before Mulgrew conceded another penalty for a trip on substitute Jakub Kosecki, this time Fraser Forster saving Vrdoljak's spot-kick.
However, Kosecki slotted in a pass from Lukasz Broz to leave next week's return game at Murrayfield in Edinburgh a pivotal one for Deila, who is facing the dispiriting prospect of dropping into the Europa League.
It was a night that brought back memories of Gordon Strachan's ill-fated first competitive match in charge against Artmedia Bratislava, when Celtic lost 5-0 to the unheralded Slovakian side in 2005. Strachan's side crashed out of the Champions League after they failed to overturn the deficit in the home leg.
While the task at Murrayfield is not as daunting as the one faced by Celtic nine years ago, they face the very real possibility of exiting before they reach the group stages. They will take heart from their 3-0 win against Shakhter Karagandy in last season's play-off following a 2-0 reverse in the first leg. But, if they perform as they did here, they have no chance of taking their place in Europe's most presitigious competition for the third successive year.
Afterwards the Norwegian said: "It was a very poor performance and worst of all was the commitment, the energy, I need much more energy in the game. We didn't stay together for 90 minutes. We started well and got the first goal but then gave way to pressure and we lost our heads and started giving the ball way in midfield so many times and mistakes in the back four, some were high, some were low, instead of being together.
"But what is done is done, we have to learn from this very quickly, we got the away a goal and we still have a chance. It is possible to win 3-0 again - like we did last year in the play-off - with the help of the supporters and we will do everything we can to do that.
Deila vowed to make himself much clearer in his instructions ahead of the second-leg in Murrayfield. He said: "It was not the plan to go forward at 2-1. We had a spell when we had good control but started making stupid mistakes and they got space behind us. That is my responsibility. I have to be much clearer as to what I expect and how we perform as a team, defensively and offensively and tonight we lost our heads and that is not good enough."
He was not too harsh on Ambrose whose defending had been poor before he was dismissed.
He said: "It is not only that situation, it was a consequence of many situations. We lost the ball too much in middle, the back four was not together and when we lost the ball we were too open. We made it difficult for ourselves and in the end they got a counter-attack and Efe went in, but it was a more of a consequence of bad defending."
Deila's counterpart, Henning Berg, was pleased by the way his side kept going despite the disappointment of missing two penalties.
He said: "We didn't feel sorry for ourselves we pushed and got more goals and we could have scored more. It is not normal to miss two penalties, especially for Ivica as he has never missed for me."