The Scottish champions, who had been outclassed 6-1 by Legia Warsaw in their third qualifying round match, had been handed a reprieve when the Polish champions were thrown out of the competition for fielding an ineligible player.
However, Celtic wasted their chance as they were sent packing for a second time when a Tavares goal handed Maribor a 1-0 win in Glasgow to earn the Slovenian champions a 2-1 aggregate win in their play-off match on Tuesday.
It was a fourth defeat in just nine competitive matches for Deila, who was criticised for making 10 changes in the 1-0 loss to Inverness last weekend, and the Norwegian was damning in his verdict of his side.
"I think we are better now than we were against Legia but we are a long way from Champions League level," he said. "When you have two chances and you don't take them then there are no excuses.
"In the end we got what we deserved. We have to be honest. We haven't been good enough and didn't deserve to go through to the Champions League; that's the truth. That's the level we are at all now and that's the level we need to work up from.
"Of course it is very disappointing and this feeling I have to take with along with the players, the staff and the whole club. We haven't deserved to be in the Champions League and we have to start building now."
A couple of hundred disgruntled Hoops fans gathered at the front doors of Celtic Park following the defeat to vent their anger at the players and the club's board of directors for a perceived lack of investment in the playing squad.
The defeat means Celtic, who had been looking to qualify for the group stage for the third year running, have lost out on a potential £20million cash boost from the competition and heaps pressure on Deila early in his Celtic career.
However, the Norwegian said he expected to add more players to his squad before the end of the transfer window. "I really understand the fans' anger," he said. "The only thing I can do is assure them that we are going to work really hard every day now so that next year we can hopefully stand in the same position next year with a whole other feeling than we have right now.
"The club wants to invest in players but we have to agree on things. I've come straight in and I've only been here a short time. It's very difficult to get the quality of player that I know the fans want to get and I want to get as well with the salaries we pay.
"But I think in this window we are going to have a signing or two more. We need now to build up the team so we can handle this situation next year. In the autumn we are going to see a bigger and better squad. Now it's Europa League and we're going to do everything we can to achieve things in that competition."
His Maribor counterpart Ante Simundza was delighted after leading his side to the group stages for the first time since 1999 and suggested the pressure the home fans placed on their own side had helped his side to victory. "The feeling I have is phenomenal and we did what we intended to do," Simundza said.
"At Celtic Park it is very hard to play for every team - the home team as well - because the fans put a lot of pressure on them. The home fans are very tough and always want their team to win. I played on this and it was good for us."