Danny Drinkwater and Ahmed Musa both went to ground in the area during the two sides' 0-0 draw but the Gunners feel the referee was correct to wave appeals away.
Arsenal defenders Laurent Koscielny and Rob Holding rejected suggestions Leicester City deserved a pair of penalties during the goalless Premier League draw at the King Power Stadium.
The top two from last season remain winless after their opening-weekend defeats and a drab stalemate short of goal-scoring chances on Saturday.
The outcome might have been different had Mark Clattenburg seen merit in penalty claims from Leicester midfielder Danny Drinkwater and substitute Ahmed Musa during the closing stages of each half.