Mourinho's Manchester United side face Ajax in the Europa League final, three days after their meaningless final league game.
United finish their league campaign at home to Palace on Sunday, three days before they face Ajax in the Europa League final in Stockholm.
Regardless of the result at the weekend, United will finish sixth while Palace cannot be relegated.
Following United's goalless draw at Southampton on Wednesday, Mourinho said the Palace match should have been brought forward at least a day to give his side the best chance against Ajax.
"They (the Premier League) could easily have changed it last week and said, 'We will give you the best chance to try to win the Europa League,'" Allardyce said Thursday.
"It's a great shame that we are not like other countries, who will bend over in fixture terms to help their teams win European competitions."
The former England manager added: "We've all been moaning about the fact we're not getting anywhere near the Champions League or we're not getting anyone winning the Europa League.
"When you look at Jose's fixture list, this will be his 63rd game (of the season) on Sunday."
Mourinho said after Southampton that he saw no point in making a last-minute plea to league chiefs to move the game and plans to blood several youngsters against Palace.
Allardyce, asked if he too would field a weakened team were he in Mourinho's position, replied: "No doubt about that. The XI that play at Stockholm would probably not feature at all in this last game."