Morata was strongly linked with a move to Old Trafford before the Red Devils secured a £75m deal for Romelu Lukaku, who made the switch from Everton.
Mourinho has said that United's interest in Morata 'was obvious and public', but the two teams could not "come to an economic agreement" for the 24-year-old, who has also been linked with Chelsea.
"I don't like to speak about players who aren't ours, because Morata is not our player. I am nobody to speak about players from Real Madrid," Mourinho told reporters.
"Yes, we have had interest, that is obvious and it's public. We have not come to an economic agreement, that is obvious as well. But it's a Real Madrid's right to ask for their players the amount of money that they want. We do not determine what the price is of a player of Real Madrid, Real Madrid do that. And we didn't arrive at an agreement with Real Madrid.
"I do not criticise Madrid and I am not going to criticise my board because my board has made the offer, and they have tried to reach an agreement during a time, and they didn't come to an agreement. It's simple."
Mourinho, speaking on the club's pre-season tour of the United States, has also revealed that he wants to sign two more players in this summer's transfer window.