Dyke hit out after the FA rejected Brentford's appeal against the red card shown by Attwell to striker Nathan Elder for an alleged elbow against Notts County on Saturday.
"This is the first time in all the years I have been involved in football that I have been compelled to speak out about a refereeing decision," Dyke told his club's official website.
"But following the announcement received in response to our appeal, everyone at Brentford finds the decision incomprehensible. There was not a person in the ground that I met from either Brentford or Notts County who believed the decision of the referee was fair or reasonable.
"One wonders what you have to do to win an appeal at the FA, who seem to be intent on trying to protect this particular referee who has already made one of the most notorious decisions in years when allowing the phantom goal for Reading against Watford earlier this season."