Asencio was convicted last month after being found to have been more than three times over Spainâs legal alcohol limit during an incident on August 16. He was fined 14,400 euros and banned from driving for eight months.
The 23-year-old is also due to appear in court in Gran Canaria this week in connection with an alleged non-consensual sharing of a sexual video dating back to 2023. Asencio denies wrongdoing in that case.
Mourinho said he was disappointed with the defender, despite praising his professionalism at Real Madrid.
"He's a model professional. When he was fit, no one trained as hard as him," Mourinho told reporters.
"Now that he's been injured for a few weeks, he's the first to arrive and the last to leave training.
"But a Real Madrid player remains a Real Madrid player 24 hours a day, seven days a week, 12 months a year.
"Everything you do outside the pitch represents Real Madrid and could affect the club's prestige.
"I'm not happy. Everyone makes mistakes but when they pile up, it's not the same."
Asencio has been sidelined with a hamstring injury since July and has yet to make Mourinho's matchday squad this season.
He was an important member of the Real Madrid squad during the previous two campaigns, making regular appearances at centre-back.
Real have now begun their own disciplinary process while Asencio faces further legal proceedings in Gran Canaria.