The club were charged after fans entered the pitch to celebrate the quarter-final win over their rivals before goading Villa fans in front of the away fans' section.
Blues have accepted the charge and will have an FA hearing scheduled for March 28th.
A club statement read: "The club continues its close work with the police with a view to identifying those responsible for threatening to tarnish the reputation of the club and Birmingham City's image."
The statement continued: "Acting Chairman Peter Pannu takes this opportunity to remind all fans that similar incidents should not occur again and is confident we have all learned a lesson from it - both the club and those who breached the rules.
"Club officials would like to thank the FA for their assistance and communication prior to and during the investigation."