United have nine games in April that will go a long way to deciding whether they qualify for next season's Champions League.
They can achieve that goal by finishing in the top four of the Premier League or by winning the Europa League, in which they play Belgium's Anderlecht in the quarter-finals.
But United manager Mourinho has revealed that England defenders Phil Jones and Chris Smalling, both injured in training with the national team this week, are set to be long-term absentees.
And, with record signing Paul Pogba struggling to recover from a hamstring problem, Mourinho has challenged his remaining players to step up.
"They have to be resilient, they have to be professionals," Mourinho said.
"They have to be team players, they have to go to the limits, they have to play with small injuries, they have to play with pain, play with fatigue because there is no other chance.
"When I look, for example, in two weeks we are going to play against Chelsea. Before, we play Anderlecht and after, we play Anderlecht.
"Chelsea, before they are on holidays and after they are on holidays. You can name their team, you can say 'This one, this one, this one, this one and this one'.
"In 15 days' time maybe the Premier League is not important for us, maybe it is.
"If we keep winning matches now, that match against Chelsea is an important match for us. If we lose matches now, that match is not important; then the important matches are only Anderlecht.
"They have to cope with everything like they did in that week against Rostov, coped with the bad pitch, coming from London by bus, they coped playing against Chelsea with 10 men, coped with playing against Rostov three days later.
"But some bodies they felt it. Like Pogba's body felt it and had a negative reaction. So we need to be strong and need to believe."
Go to the beach
Having apparently indicated in midweek that both Jones and Smalling will not play again this season, Mourinho now claims that they are merely "long-term" injuries, although he would not be specific over Jones' toe problem and Smalling's calf injury.
Mourinho is also without the suspended Zlatan Ibrahimovic and Ander Herrera as United start April with a league game against West Bromwich Albion on Saturday.
Given the schedule facing United, Mourinho, not surprisingly, would not be drawn on his summer plans, but he was adamant on one point, that any players on his wanted list - a group understood to be headed by French international striker Antoine Griezmann - will have to be committed to United.
The assertion supposedly made this week, for example, by Arsenal's Alexis Sanchez that he wants to remain in London would not wash with the United manager.
"If a player wants to move to London, enjoy London, we don't want you," said Mourinho.
"If the first thing you think is where you're going to live - think Los Angeles, Galaxy would be the first choice, then (Portuguese side) Vitoria Setubal, go to the beach every day.
"There are beautiful places to live and to play. We want people who are dreaming about coming (to United)."