Berg reacted with fury after UEFA ruled the Polish champions had fielded in ineligible player in their 2-0 second leg defeat of Celtic at Murrayfield on Wednesday.
The victory completed a 6-1 aggregate win and should have secured Legia a play-off place before the game's governing body claimed their defender Bartosz Bereszynski had not been properly registered.
Bereszynski had been sent off against Apollon in the final match of Legia's Europa League campaign last season and was handed an automatic three-match ban. He missed both ties against St Patrick's in the second qualifying round and then sat out the first leg against Celtic.
But UEFA decided he had not been registered in Legia's squad for the games against the Irish side in order to allow a three-match suspension to take effect.
Speaking to Sky Sports News, Berg said: "We will appeal this, definitely. We will go as high as we can because we do not think this is the right decision.
"We are absolutely shocked at this decision. For UEFA to make this, with the consequences of it for what has happened, is unbelievable.
"We have a player from last season playing in the Europa League being suspended for three games after a red card. This season he did not play the first two games against St Patrick's and the first game against Celtic and then he was ready for the fourth game.
"He should have been ok. The technical mistake which our administration made was not to put him in the squad for the two first games against St Patrick's for him to serve his suspension.
"And this little technical mistake for him not being on this paper without even playing has taken away our chance of getting into the Champions League which would have been a dream for this club and these players who have worked so hard for us to get to this position.
"He has been registered to us for all this time so we were not trying to hide anything. This has been open and this is just a little small technical mistake in the administration and the consequences for us now is very, very difficult to take."
And Berg has called on UEFA to show consistency, pointing out they have used different punishment for similar offences in the past.
"I think this goes against every intention of fair play and fair competition and I think there has been a case like this before.
"In 2010 Debrecen from Hungary also used a player and their case was not even as strong as ours and UEFA told them because they acted in good faith the result stood and it was not affected.
"So for them to make a different decision this time with consequences like this is very, very difficult to take. European football should be about fair competition and fair play.
"The financial implications of this impact hugely on the club, on how we want to build it in the future. We are progressing as a club, we have won the league two years in a row and we are building for the future and I feel for the players who have worked so hard to get us to this position.
"There has not been a Polish team in the Champions League for 17 or 18 years and we felt we had a good chance to get to it and it has been taken away from us because of this technical mistake and the decision from UEFA."
Legia chairman Boguslaw Lesniodorski believes Celtic should have refused to accept the ruling after being so convincingly beaten by their Polish rivals.
“I’m very disappointed, once again football and sport lost," he said. "We hope that Celtic will react and follow fair play rules. For us what happened on the field matters.”
Following the decision, Legia were placed into the final qualifying round for the Europa League where they were paired with Aktobe of Kazakhstan, while Celtic were drawn against Slovenian side Maribor in the Champions League play-offs.