The Blues play Tottenham in the domestic trophy semi-final before commencing the first leg of their European semi-final against Barcelona three days later on April 18.
The cup fixture has been set for a late afternoon kick-off on the Sunday, which could harm the west London club’s chances in their home clash, with the reigning Champions League victors expected to have their La Liga commitments scheduled for the Saturday.
Di Matteo told reporters: “I'm very disappointed that common sense hasn't prevailed in this.
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“Obviously, they didn't take into consideration anything that we said.
“Barca will have one more day to recover than us and it might give them a little advantage.”
The French federation, for example, has been known to reschedule Ligue 1 fixtures to help give competing sides the ability to freshen up before crucial ties, a truth that Di Matteo has lamented.
“Other federations are very helpful,” Di Matteo continued. “The English federation hasn't seemed very helpful in our case.”
The FA declined to comment on the subject.