Lukaku, 24, had been widely tipped to return to Chelsea before United paid an initial £75m for the Belgian international.
Mourinho has denied suggestions that his personal relationship with Lukaku was key in completing the signing, with the Portuguese admitting that the 20-time English champions were simply prepared to offer a better deal.
"I don't think it was my influence, no. I think that we paid the money that Everton asked for and we paid the player the wages that his agent asked for and we paid the agents the commission that they asked for. I don't see another reason," Mourinho told reporters.
Lukaku has scored six times in six appearances for United at the start of the 2017-18 campaign.