McGeady was fined two weeks' wages and banned for a fortnight
Aiden McGeady will not dispute the fine and first-team suspension imposed by Celtic for a breach of club discipline.
A dressing-room row with manager Gordon Strachan cost the 22-year-old two weeks' wages and saw him banned from playing for a fortnight.
McGeady was available at the weekend but was not selected by Strachan.
A players' union statement read: "It is his wish that this brings this matter to a conclusion and his desire is to get back playing for Celtic."
The Republic of Ireland midfielder, who is refusing to comment further, was entitled to consider a defence against the sanctions taken against him but has chosen to let the matter rest.
"He has used this time in the proper way which has allowed him to take due consideration to all the facts and circumstances regarding the matter," added the PFA Scotland statement.
"After lengthy discussions with his family and advisors Aiden has decided not to appeal the penalties imposed upon him by Celtic F.C."
PFA Scotland chief executive Fraser Wishart said: "Aiden McGeady has conducted himself throughout this situation in a thoughtful, measured and mature manner.
"Aiden has rightly taken time to consider his position and will continue to have the full support of PFA Scotland."
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