The Red Devils can still secure a top-four finish in the Premier League this season, but a 2-0 defeat to Arsenal means their fate is no longer in their own hands.
United hold a slender 1-0 lead in their semi-final clash with Celta Vigo ahead of a return date at Old Trafford on Thursday, but their manager remains calm despite there being no guarantees that an expensively-assembled squad will be back among the continental elite next season.
Mourinho told ESPN Brazil: “There’s no pressure.
“We tried. We tried with everything. We try first to get to the final, then if we do it, we try to win the final. The pressure is normal.”
Mourinho is expected to bring his big hitters back in for a midweek meeting with Celta, with United now being careful not to expose the likes of Paul Pogba, Marcus Rashford, Eric Bailly and Antonio Valencia to unnecessary domestic outings.
“Now, it’s impossible for the players to play all the games,” added Mourinho.
“It’s impossible for the players to play on Thursday, on Sunday, on Thursday, on Sunday like they’ve been doing all season.
“I want to give the players the conditions to compete on Thursday with a team that is resting all of their players in the Spanish league.
“They rest eleven, I rest eight. We’re going with everything on Thursday.”
United’s cause has been aided by the fact that Juan Mata, Chris Smalling and Phil Jones have all returned to action after spells on the sidelines, with all three involved against Arsenal.
Mourinho does now have more options at his disposal, but he has already suggested that he will include a number of youngsters in his Premier League plans if United are able to reach the Europa League final.