AEK, who dropped from the top flight last week, were docked three points from this season and fined 4,000 euros after the April 14 match at home to Panthrakikos was abandoned when home fans chased both sets of players off the pitch.
Panthrakikos were awarded a 3-0 win for the match, which was stopped after AEK had conceded an 87th-minute goal to go 1-0 behind against their fellow strugglers.
AEK, who will start next season in the second tier with a further two points deducted, had been fighting to at least get the chance to play the final three minutes of the abandoned match.
"The EPO court of appeal has accepted the punishment administered by the Super League and rejects outright AEK's appeal," the federation said in a statement.
The sanction led to AEK being relegated for the first time in their 89-year history.
AEK are the second club to receive such a penalty, following Panathinaikos who received the same five-point deduction after last season's derby with Olympiacos at the Olympic Stadium was abandoned.
The decision closes the book on the club's most turbulent season.
AEK have been operating on a shoe-string budget following a period of financial turmoil in which virtually the entire first-team squad was sold off in order to secure a licence and preserve their top-flight status.
Club officials have been seeking new investors but after the recent collapse of a potential deal with London-based investment bank Seymour Pierce, their efforts have been unsuccessful.
Groups of supporters have staged regular protests at the training facilities due to the state of the team's finances, while the Nazi-salute goal celebration of midfielder Giorgos Katidis last month provided another blow to AEK's reputation.
Katidis was banned for five matches, fined 1,000 euros and also received a life ban from all national teams by the Greek Football Federation for making the gesture after scoring the winning goal in a 2-1 league victory over Veria.