A total of 20,000 pounds of the fine will be suspended until the end of the 2013/14 season.
The Premier League club admitted a charge of failing to ensure no spectators or unauthorised persons encroached onto the playing area.
Five people were arrested after the pitch invasion following Birmingham's 2-1 quarter-final win. City beat Arsenal 2-1 in the final in February, securing their first major trophy since 1963.
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