The Hoops were stunned at Parkhead last night as Tavares' strike on 75 minutes sent NK Maribor into the group stage and the hosts tumbling into the Europa League.
Ronny Deila's side spurned several chances over the 90 minutes only for the Slovenians to nab the goal to clinch a 2-1 aggregate win.
It means Celtic will miss out on a third successive stint in Europe's elite competition with Maribor netting the £20million windfall that comes with qualification.
And Parkhead forward Berget, who started on the left flank in favour of Kris Commons last night, refused to accept Deila's men were unlucky not to progress over the two legs.
The Cardiff City loan star said: "It's difficult. It's not at all what we hoped for. This is where we are now, not good enough, and we need to use the league and the Europa League to get better and hopefully be better next year.
"We didn't win over two games, so we're not unlucky. We had our chances here, we could have and should have put them in which would have taken us through.
"We were not able to control the match like we wanted to, especially in the first half.
"We fell deep, we didn't work the ball or keep it well enough and the pressure was a little bit here and there. We didn't settle and nothing worked.
"In the second half we started better. We played a bit higher and managed to get some pressure, but we didn't put it in."
Emotions spilled over following full-time as hundreds of fans gathered to protest outside the main door of the stadium.
Chants of "Sack the board", "Where's the money gone?" as well as jibes directed at chief executive Peter Lawwell rang outside Parkhead as the SPFL Premiership holders now face a season without Champions League football.
And while Berget empathised with the fans' frustrations, the Norwegian vowed that the players will do all they can to put things right.
He said: "Of course we understand the fans being angry. They want to be in the Champions Leauge and so do we.
"We're not happy about this but that's the way it is right now. We just need to stand together and work from there.
"It's just something we need to do. You need to back each other up and everyone needs to work together to show we are a good team.
"It's going to be hard but it's our job."
Speaking about the side's preparations and tactics for the game, he added: "It's up to the manager and of course he didn't want us to look as we did in the first half.
"That wasn't the plan. It's not about the tactics it's about how we worked."