The tie on April 15 at Wembley will kick off at 6pm, giving the club precious little time to prepare for Wednesday's first leg of a Champions League semi which they can book by finishing off Benfica in the quarter-final next week.
The other FA Cup semi-final between Everton and Liverpool, also at Wembley, is being played the day before so as not to clash with the 23rd anniversary of the Hillsborough tragedy.
"First of all we have to qualify for the semi-final, but on the other hand we have tried to communicate with the FA and co-operate, so it's disappointing, I would say, that common sense hasn't prevailed," caretaker boss Di Matteo told reporters.
"I probably would have been happy with a Friday night kick-off. We have tried to co-operate with the authorities and given our point of view but it seems it hasn't been taken into consideration."
Before their cup exertions, Chelsea's immediate task is trying to close the five-point gap on Tottenham in the race for a top-four finish in the Premier League and a Champions League berth for next term.
Di Matteo must juggle his squad with an eye on the second leg against Benfica on Wednesday, when his side defend the 1-0 lead they gained in Lisbon this week.
With Tottenham not playing until Sunday against Swansea City, Chelsea can put pressure on the North London side with victory at Aston Villa on Saturday.
"I am only focusing on Saturday and then we will think about the next one. I have to assess the players tomorrow morning and try to select a team that is ready and strong to win at Villa," said Di Matteo, who surprised pundits by picking Fernando Torres among others against the Portuguese.
Right-back Branislav Ivanovic is fit for the trip to Villa after he missed the last two matches but Raul Meireles is unlikely to be risked.
"Ivanovic will be available for tomorrow, he has come through training fine," Di Matteo said.
"The only doubt is Meireles who picked up a knock the other night [in Lisbon], everybody else is OK. He's got a knock just above his knee so it shouldn't be too serious but he's not ready for tomorrow."
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