Pogba, 24, was taken off after 18 minutes at Old Trafford in Manchester United’s opening Group A win over Basel last night.
United manager Mourinho admitted after the 3-0 win that Pogba is expected to be sidelined for “a few weeks”, although further assessment is required on the Frenchman who left Old Trafford on crutches.
And Rashford believes United will understandably miss Pogba in midfield, but feels Mourinho has enough strength in depth to cope without him.
"That's why you have such a strong squad," the 19-year-old forward said.
"It's good for the manager, it's good for the players as well because we're always playing for competition.
GETTY
Marcus Rashford says Manchester United can cope without Paul Pogba
That's why you have such a strong squad - it's good for the manager
Marcus Rashford
"But Paul's going to be a massive miss and hopefully we can get him back fit as soon as possible.
"We have to play every game to win. If we want to be champions, then we have to win them types of games (like Sunday's).
"It's going to be difficult. Everton are a really strong team.
"They made some good signings in the summer and you know they've got strength all around the pitch so we have to come here and try and get the result."
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Rashford has looked bright in the early weeks of the campaign but has been unable to nail down a starting berth due to impressive attacking options.
But the teenager, who added to Marouane Fellaini and Romelu Lukaku’s goals against Basel, believes healthy competition for places is helping his development.
"It's difficult when you're in and out of the team, but we have to find the positives out of it and I think we have both done that," Rashford added.
"I think the competition is always positive competition because we're improving each other every day when we're in training and in the games we're pushing each other more and more.
"It's a bit of a headache for the manager but it is a good headache to have."