United dropped points at Old Trafford for the 10th time this season as Gylfi Sigurdsson's late free kick further dented their chase for the top four.
They could still qualify for next season's Champions League via the Europa League but head into the first leg of the semi-final against Celta Vigo on Thursday shorn of four key defenders after Eric Bailly was forced off in the second-half on Sunday.
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Bailly joins Phil Jones, Chris Smalling and Marcos Rojo on the sidelines with Daley Blind the only available central defender ahead of the trip to Spain.
"At the moment we can’t walk from the bed to the toilet without breaking a leg,” Mourinho said after the game.
United have reached the latter stages of both domestic cup competitions as well as the Europa League and Mourinho believes the fixture pile-up that would come with reaching the final in Stockholm could force him to make sweeping changes against Crystal Palace on the final day.
"It’s a consequence of our success, but also of the calendar,” he added. “You are punished for doing well.
"At the moment this is hypothetical, but if we beat Celta [Vigo], we have the final. But the Europa League final is on the Wednesday (May 24) and we play Palace on the Sunday, and Southampton a few days before that (on the 17th).
"We could be playing the final with disastrous consequences.
"Maybe I will bring Nicky Butt and his team to play against Crystal Palace. And hopefully Palace doesn’t need to stay in the division, because it would be very bad if they needed the points and we played our Under-23s."