Legia request for provisional measures that would have allowed them to take part in the play-off round pending an appeal was rejected by CAS.
The Polish club beat Celtic 6-1 on aggregate in their third qualifying round tie but were knocked out of the competition when UEFA ordered that they forfeit the second leg, which they won 2-0, for fielding an ineligible player.
The Scottish side were awarded a 3-0 win, which allowed them to qualify on away goals with a 4-4 aggregate draw.
Legia had appealed against the decision to CAS and asked for urgent provisional measures so they could have taken part in the play-off round.
The CAS ruling means that Celtic will face Slovenian champions Maribor over two legs for a place in the lucrative group stage, with the first leg in Slovenia on Wednesday and the return on Aug 26.
"The president of the CAS appeals arbitration division considered the parties' written submissions and has denied Legia Warszawa's request," the Lausanne-based tribunal said.
"The CAS arbitration will now continue and a panel of arbitrators will be constituted to examine this case within the next weeks.
"On the merits, Legia has requested that no sanctions be imposed on either the club or the player, (Bartosz) Bereszynski, and that UEFA be ordered to pay a financial compensation to the Polish club."
Legia brought on Bereszynski, who was suspended, for the last few minutes of the second leg against the Scottish champions at Murrayfield.
Legia, who last qualified for the group stages in 1995/96, thought Bereszynski was eligible but because he had not been registered in their squad for their previous three matches he had not completed the ban.
Legia also missed two penalties in the first leg, which they won 4-1.
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