The 21-year-old said he regretted his reaction, which resulted in a two-game suspension, and he would have to learn his lesson.
"Suppose I will just have to take the abuse about my kids in future," Wilshere said on his Twitter account.
"Anyway, one more game to go! Can't wait to be back."
Having missed second-placed Arsenal's goalless draw with Chelsea on Monday, Wilshere will complete his ban by sitting out Thursday's Premier League visit to West Ham United.
The player will be back for the match at Newcastle United on Sunday.
Arsenal were beaten 6-3 by City at the Etihad Stadium on December 14.
(Reporting by Tim Collings; editing by Tony Jimenez)
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