Wilshere was handed a two-match suspension from the Football Association for making the gesture during the second half of Arsenal's 6-3 defeat at the hands of City at the Eithad Stadium.
The punishment sidelined him for Monday's goalless draw with Chelsea and will keep him out of the Gunners' Boxing Day clash with West Ham at Upton Park.
On Tuesday Wilshere explained his actions on Twitter and admitted he may have to be prepared to suffer similar attacks from the stands in future.
"Gutted not to be Involved last night! Shouldn't of [sic] reacted the way I did but I know all you dads out there love your kids the way I do....," he wrote.
"Suppose I will just have to take the abuse about my kids in future......anyway, one more game to go! Can't wait to be back! #AFC"