The 20-time English champions have brought in Victor Lindelof, Romelu Lukaku and Nemanja Matic since last season for a combined fee of close to £150 million (A$240 million)
Mourinho had also wanted an extra winger but United's pursuit of Inter's Ivan Perisic has failed, while reported interest in Real Madrid star Gareth Bale also proved fruitless.
The Portuguese boss is ready to accept defeat in his hopes for a final signing but insists he is happy with the squad at his disposal and the effort made by executive vice-chairman Ed Woodward.
"I told Mr. Woodward that obviously my plans were four but I also told people 'no pressure from me, do what you think is best for the club'," he told a news conference on Friday.
"We'll be together again for another transfer window in January and next summer so there is no pressure from me at all. I'm happy with the squad we have and I'm ready to go without the fourth player, so if we are out of the market, I'm fine, I'm ready."
Mourinho had earlier confirmed that full-back Luke Shaw and winger Ashley Young were close to a return to the first-team squad.
Shaw damaged his ankle ligaments against Swansea City in April and Young had surgery on a groin problem in May, with neither able to make an appearance in pre-season.
However, Mourinho expects both to be available again soon if they are able to come through an Under-23 match on Monday unscathed.
"Everybody is fine. The next week, on Monday, in the Under-23s game, Luke Shaw and Ashley Young are playing their first minutes of competition this season," he told MUTV.
"It is like a pre-season match for them. But it is good news because, when they can play with the Under-23s, it is because the last week they trained with us all week so they are both coming [back]."