Mats Hummels (C) remonstrates with English referee Michael Oliver (L) during Dortmund s defeat to Ajax in the Champions League (AFP)
Hummels, 32, was sent off just 29 minutes into Dortmund's home defeat on Wednesday after a clumsy tackle on Ajax forward Antony.
English referee Michael Oliver consulted the video assistant referee but did not consult the footage himself and stood by his decision.
"This is a total injustice, we feel punished enough by the outcome of the match," managing director Hans-Joachim Watzke told AFP subsidiary SID.
"We appeal to UEFA's sense of justice - to set an example here and not punish the player as well."
Dortmund sports director Michael Zorc said he has already made contact with UEFA over the sending off, which he said was "more than obviously - and clearly provable - a wrong decision. It ruined our game and decided the match".
Despite being a man down, Dortmund went ahead when Marco Reus converted a penalty before Ajax scored unanswered second-half goals by Dusan Tadic, Sebastien Haller and Davy Klaassen.
The German club is checking with its legal advisors and Zorc could not mask his frustration.
"UEFA promotes respect, but this has nothing to do with respect," Zorc fumed.
"Oliver stood ten metres from the (video replay) screen, which he should have watched. Mats slid 40 centimetres past Antony and caught his foot."
Hummels has said he expects to be suspended for their next Champions League game against Sporting Lisbon on November 24 which could be decisive in Dortmund's chances of making the last 16.
Ajax are into the knock-out stages after four wins from four, leaving Dortmund level on points in Group C with third-placed Sporting, who hammered Besiktas 4-0 Wednesday.
"I have no idea how you can give red as a referee at Champions League level. For me, that is an absurdly-wrong decision," fumed Hummels.
"The game was decided by the referee and I think he knows it."
Hummels also accused Antony of milking the situation by rolling around on the turf after the tackle, "that was grossly unsportsmanlike".
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