The Spain international was vying for the ball near the touchline in the 12th minute of the second leg at Stamford Bridge when he stood hard on Can's shin as the midfielder slid to try and win possession.
Referee Michael Oliver took no action after missing the incident during the game, which Chelsea won 1-0 to progress to the final 2-1 on aggregate, but the FA has taken a dim view and decided to take retrospective action.
However, Costa will face no action for a similar stamping incident involving Martin Skrtel in the second half.
An FA statement read: "Diego Costa has been charged by The FA for violent conduct following an on-field incident which was not seen by the match officials but caught on video.
"The charge is in relation to an incident involving the Chelsea forward and Liverpool’s Emre Can which occurred in the 12th minute of the League Cup semi-final second leg at Stamford Bridge last night [Tuesday 27 January 2015].
"The player has until 6pm on Thursday 29 January 2015 to respond to the charge.
"Following a review of an incident during the game involving Costa and Liverpool’s Martin Skrtel, The FA will not be taking any further action."
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