Trailing 4-1 from the first leg of the third qualifying round in Poland last week, a difficult task for the Hoops at the BT Murrayfield stadium in Edinburgh became impossible when Michal Zyro notched in the 36th minute to dampen down expectations of a famous fightback
The Scottish champions were booed off at the interval and when Michal Kucharczyk added a second on the hour mark it was all over, meaning the Parkhead side drop into the Europa League qualifiers.
Hoops boss Deila admitted his side were simply not good enough as he contemplated improvements before the transfer window closes.
The Norwegian said: "I have to accept that is the level right now and have to work from here.
"I have a big job to do to improve as a team so we can win the league and get into the Europa League, which would be a good achievement for us.
"I have been here for six weeks but right now it is not good enough, from what I can see,
"We need to make the squad better by getting in new players but we also have to do the best with what is here.
"Right now, of course it is not good enough.
"We have injuries and I was glad to see James Forrest coming on, with his pace, so that was (a) positive on a very black day.
"I wasn't embarrassed but I am not satisfied.
"I feel sorry for the players, they wanted it but we didn't perform well enough and that is where we are."
Celtic captain Charlie Mulgrew was "devastated" following the defeat and while he claims the Hoops players are still getting used to Deila's demands, he refused to use that as an excuse.
"The whole pre-season was geared towards the Champions League," he said.
"We are not there now but we need to be as positive as we can.
"We never competed well enough
I'm not taking anything away from them but we could do a lot better
"It takes time for the manager to bed things in but we are not using this as an excuse.
"It is up to us to respond to what he wants us to do and quickly.
"It is devastating but we all have to pick ourselves up quickly."
Legia Warsaw boss Henning Berg backed Deila, claiming his fellow Norwegian has got what it takes to bounce back from such an early setback in his Hoops career.
The former Rangers defender said: "I know him a little from Norway
He has the experience, the knowledge and character
"I hope Celtic give him time
That would be a wise thing to do
"To get his ideas into the team in one month is very difficult.
"To play the important games so early in the season is difficult, we know that at Legia."
Berg, though, preferred to concentrate on the strengths of his side rather than the shortcomings of Celtic when analysing the match.
He said: "Our team did really well.
"We are a strong team, with good technique.
"I am sure they will say that Celtic didn't play well but I look at my team and say that we made them play not so well.
"It is more that we played well than they played badly.
"We showed we have a good team with good potential who are working well together.
"We came with a lead and were solid and dangerous on the counter-attack
I am happy we were able to stop them scoring and making so many chances
This is a big step for us."
Source : PA
Source: PA