UEFA's appeals body had met on Wednesday morning to listen to the Polish champions' arguments over the registration error that turned their 6-1 aggregate win over Celtic into an away-goals defeat.
Legia had fielded Bartosz Bereszynski as a substitute in the closing minutes of their 2-0 second-leg win at Murrayfied in the belief that he had served a three-match ban - only to discover they had not registered him in their squad for the previous round.
Legia plan to take their case to the Court of Arbitration for Sport after failing at UEFA.
The second leg and tie was effectively dead before kick-off due to Bereszynski being on the bench as a suspended player.
UEFA rules dictate that a team fielding a suspended player would forfeit the match with a 3-0 defeat. They therefore lost the second 3-0 leg sending Celtic through 4-4 on away goals.
Legia had called on UEFA to follow its own "football first" principle when their appeal against their effective Champions League expulsion was heard.
The club had previously accused Celtic of ignoring their telephone calls and emails on the day of the first hearing after Zbigniew Boniek, the legendary player who now runs Polish football, claimed Legia would have kept their place with Celtic's consent.
Polish sources said Legia were happy to have a meeting with Celtic officials in Glasgow or Warsaw to discuss the matter.
Henning Berg's side must console themselves with a Europa League qualifier against Aktobe on Thursday night.
"Having UEFA overturn its decision, we felt for the sake of football this would be the best result. Unfortunately it appears that procedures are more important," Legia co-owner Dariusz Mioduski told Sky Sports.
"We believe this is not just about Legia but football generally and the sense of fairness and justice.
"We will have to adopt the fast-track method because our intention is to reinstate us before the Wednesday (Champions League fourth qualifying round) games so we will work today and tomorrow to launch the appeal and hopefully by Monday we will have the result."
- Sports & Recreation