A 1-0 play-off defeat by Maribor at Parkhead on Tuesday night took the visitors into the group stages of European football's premier club competition, 2-1 on aggregate.
The Hoops were beaten 6-1 on aggregate by Legia Warsaw in the third qualifier but were reinstated after the Polish club were effectively thrown out by UEFA for fielding a player who should have been suspended in the second leg at Murrayfield.
The Scottish champions were confident of reaching the group stages of the tournament for the third successive season after a 1-1 draw in Slovenia last week.
However, Maribor skipper Tavares grabbed the crucial goal in the 75th minute which cost the Parkhead club around £15million to £20million in revenue - but much more in reputation as the spotlight falls on Deila.
Celtic drop into the Europa League but that will do little to enthuse Hoops fans who vented their anger at the final whistle with some protesting outside the main door.
Deila, who took over from Neil Lennon in June, said: "The first half wasn't good enough, we were more aggressive in the second half and it was a very even game.
"They had two chances before the goal came and they were more effective.
"At the end, there is only one thing to say, we haven't been good enough and we haven't deserved to go to the Champions League.
"There is no excuse. We are not good enough. Now it is the Europa League and we will do everything we can to achieve things in that competition.
"That is our level now and that is what we have to work from.
"We didn't lose because of the defending, we lost because we didn't create anything.
"We have to have more tempo and movement in our play, that is the job and it has to start now."
Deila added: "I really understand them (fans) and the only thing I can do is assure them that I will work hard every day so we will be in a better situation next year and be happy at this moment.
"We have to be honest. We haven't been good enough and that is the truth.
"I thought we had a good enough team to go through but we didn't do it."
The Norwegian is set to sign Rubin Kazan winger Wakaso Mubarak with discussion on-going with Sporting Gijon's Serbian striker, Stefan Scepovic.
"It has been a short time," he added. "Things have been happening quick and I know that we will be a good team but we need some signings.
"We have been a little bit unlucky with injuries. We need a bigger squad and better squad.
"The club wants to invest in the team but we have to agree on things.
"I have been there for a short time and it is very difficult to get the quality of players that the fans and I want to get with the salaries we offer.
"But I think we will have signing or two more and we will have done a lot in this window."
Maribor boss Ante Simundza, who played for the club when they were last in the Champions League in 1999, spoke about a "phenomenal" result for his side as he claimed Celtic played the way he thought that they would.
"I expected what I saw today from Celtic tonight," he said.
"I knew that they would not go immediately to put us under pressure, that they would wait for the second-half and they did exactly that and I was confident that we could score to get the win to get to the group stages.
"Getting there is very important for us and our fans and it is a great thing for Slovenia."