Dugs, who was shown two yellow cards in the 4-0 defeat to Graeme Souness' side in December, was charged with violent behaviour by the FA last week for an alleged elbowing offence on centre-back Short.
The referee on the day, Graham Barber, did not see the incident but video evidence was used by the FA to come to their decision.
The French forward, who is currently sidelined with a knee injury, will be suspended for the next three Blues games - Chelsea (a), Wimbledon (h) and Newcastle (h).