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 said.
"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."