After stewards demoted Sebastian Vettel from second to fifth place for his late-race pass on Jenson Button, Dr Helmut Marko admitted it had left an "aftertaste".
On Monday, he suggested the governing body often applies a "double standard", punishing some for identical infractions and not unnamed others.
Speaking on Red Bull-owned Austrian television Servus TV, the energy drink company's motor racing chief said the Vettel penalty was like "the death penalty for stealing chickens".
Jean-Eric Vergne, a rookie selected by Marko for Red Bull's secondary team Toro Rosso, agreed that Vettel only left the circuit because he was forced wide by Button.
"In Sebastian's place I would have done exactly the same," the Frenchman said.
Marko also suggested the FIA 'forgot' to warn Red Bull that simply letting Button re-pass could have saved Vettel the much harsher post-race time penalty.
"That warning did not come," he revealed.
Some F1 insiders suspect there could be more to the recent 'FIA versus Red Bull' wrangling.
In Germany's Bild newspaper, it is noted that "In formula one, it is no secret that Bernie Ecclestone is on Red Bull's side".
And the F1 chief executive is "the archenemy of FIA boss Jean Todt".
At present, the sport's most powerful pair are arguing about the vital and lucrative Concorde Agreement.
Writing in Der Spiegel newspaper, journalist Ralf Bach also referred to the behind-the-scenes "power struggle", and the fact that Ecclestone runs Red Bull by "remote control".
Vettel has vowed to do his best to give stewards no possible reason to punish him this weekend in Hungary.
"I will be careful to do nothing that could jeopardise the result," said the German.