Martinez was furious at referee Stuart Attwell for the second-half dismissal of defender Gary Caldwell for a tackle on hat-trick hero Carlos Tevez.
As the match was still scoreless at the time, Martinez felt the decision had a huge bearing on the outcome, which put City back in contention for a top-four spot, whilst at the same time leaving Wigan in the relegation dog-fight.
If anything, the Latics chief felt Tevez had been the transgressor and felt Attwell could not have seen the incident properly to reach the eventual outcome and accused the official of 'lying'.
"I cannot understand how you can give something you can't see," said Martinez.
"To give a red card you have to be certain.
"Gary said he went in really strong and got the ball. Carlos Tevez saw it and jumped off the ground, he is the one who left both feet.
"We are all human beings and we all make mistakes but to give a decision after something you don't see that is lying. You are making it up. That is hard to take.
"He (the referee) said he saw Gary Caldwell with both feet off the ground. That's why he gave the red card. But Gary Caldwell only went with one foot. That is a real injustice."
Martinez has until April 6 to respond, which is the same day City manager Roberto Mancini must answer a similar FA query into his conduct during City's recent home defeat to Everton.