The 22 year-old is likely to miss between six to nine months of action after rupturing his anterior cruciate ligament in Madrid's friendly with Arsenal earlier this week.
Asensio scored an equaliser for his side in the International Champions Cup clash - which Madrid won on penalties following a 2-2 draw - and was expected to play a key part for Zinedine Zidane's men this coming campaign, but he is instead starting a long road to recovery.
Speaking for the first time since Madrid confirmed the extent of his injury, Asensio posted a message to supporters on his social media platforms.
"I began this season with renewed hopes, looking after even the last tiny detail of my preparation so that this would be a great season for all the Madrid fans and for myself," he said.
"At the highest points in life, you can have an unexpected stroke of bad luck and suddenly everything changes. It is hard to accept everything these days, but I begin another personal challenge in my life. I still trust that this will be a great season.
"Your messages of support and loving gestures give me even more strength to face this challenge. Heartfelt thanks to all of you for your support. See you soon."
Zidane also faces being without Ferland Mendy for the start of the new campaign as the €48million signing from Lyon injured his leg in the draw with Arsenal.
Mendy's injury will continue to be monitored but he could miss around four weeks, according to reports in Spain.
Madrid begins its LaLiga campaign with a trip to Celta Vigo on 17 August.