European football's governing body awarded the Scottish champions a default 3-0 win after it was discovered that Legia fielded substitute Bartosz Bereszynski near the end of their 2-0 second-leg win at Murrayfield on Wednesday night while he was supposed to be suspended.
Bereszynski was handed a three-match ban after a red card in the Europa League last season and Legia believed he was free to play after missing the two games against St Patrick's Athletic as well as the first-leg against Celtic in Warsaw.
However, the player was not included on Legia's squad list submitted to UEFA for the St Patrick's Athletic games and thus his suspension is not served.
Consequently, Celtic went through on away goals after a 4-4 draw and were drawn against Slovenian side Maribor in the Champions League play-off.
Berg, speaking to Sky Sports News, confirmed that the Warsaw club would appeal the decision "all the way" as he struggled to come to terms with the punishment.
He said: "For UEFA to make a decision like this, with all the consequences....it's unbelievable.
"We acted in good faith. We made a mistake in administration with the papers for the St Patrick's games.
"We knew he was suspended and he didn't play in those two games or the first game against Celtic.
"He played in the Super Cup and our league games between those matches, he's been registered with us for all this time and we've not tried to hide anything.
"We've been open and it's just a little small technical mistake in the administration and the consequences for us now is that we are not able to play in the Champions League which was a dream for all our players and the club.
"It's very, very difficult to take and I think it goes against every intention of fair play and fair competition."
Legia will play Aktobe of Kazakhstan in the Europa League play-off which is scant consolation for Berg, who bemoaned the loss of possible Champions League revenue and the prestige that comes with playing against the best in Europe.
The former Rangers, Manchester United and Norway defender said: "We are progressing as a club, we won the league in Poland two years in a row and we are building and progressing.
"One thing is the money but for the players, who have worked so hard to get to this position.
"There has not been a Polish team in this competition for 17 or 18 years and now we thought we had a good chance, but it has been taken away from us because of this little technical mistake in the administration and also because of the decisions from UEFA.
"For us to get this kind of punishment, to take away the possibility and dream of these players to compete against the best players on this stage, is devastating."