Ronny Deila admitted Celtic "are not good enough" after his side crashed out of the Champions League for the second time this season.
A 1-0 play-off defeat by Maribor at Parkhead 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 found to have fielded 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.
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 the 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.
"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.