The artist published a version of the controversial DC Comics cover in the style of legendary cartoonist R Crumb on his blog.
"You are a fanboy/fangirl," March wrote in a later post. "You've got the right to criticise my work. That's the game. Cool.
"You are a colleague artist. You shouldn't do that. Because doing good art is not enough to be a good artist."
The original cover, which shows Catwoman in an awkward pose where both her face, chest and rear are simultaneously visible, drew criticism from artists when it was previewed earlier this month.
"I don't even care if that drawing is official or whatever, I can't believe someone drew it and thought it was okay to show people. People can see that drawing! People with eyes," said cartoonist Faith Erin Hick.
"Why do I even fight so hard to make my art look good when someone else drew that? As a person with eyes, I am a little offended."
The Judd Winick-penned Catwoman #1 caused controversy on its debut last year for its closing sex scene.
March was recently announced as artist on the new Batman tie-in Talon, which will debut in September.