"I feel really surprised that the decision is made before our draw in Europe because nobody knows who we play against, nor where the first and second matches are being played," Mourinho told reporters ahead of Friday's Europa League draw.
"We play Chelsea on Monday then we've got a second match in Europe, Russia or Turkey. This is what we have."
The Portuguese also criticised local rivals Manchester City, who fielded a weakened team in the FA Cup last season when faced with a similar problem under former manager Manuel Pellegrini.
Chelsea duly ran out 5-1 winners against Pellegrini's second-string selection, and Mourinho said he would not disrespect the competition by packing his side with youngsters.
"I cannot play against Chelsea with the second team," Mourinho added. "I cannot play against Chelsea with the under-21s, like Manchester City did -- was it last year? We're Manchester United. I cannot do that. I don't do that.
"As United manager, I don't do that to the FA Cup because the FA Cup is not guilty of these decisions. The cup is beautiful, the competition is historical and I have to treat United supporters and the FA Cup in the right way.
"What is going to happen is an accumulation of matches, people playing lots of matches. I will have to make some rotation but some of the boys will have to play all consecutive matches."
United, who have won the FA Cup 12 times, play Southampton in the League Cup final on Sunday, looking for their fifth win in the competition.
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
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