"In the past 24 hours I have received an overwhelming amount of love and support," she wrote. "I cannot individually respond to the hundreds of beautiful and heartfelt messages, but I see them, and appreciate you all for sending positivity to my family and I."
Perry, 52, suffered from a massive stroke he suffered last week.
The Beverly Hills, 90210 actor remained under "heavy sedation" for five days while in hospital, until he died on Monday.
"I'm not really sure what to say or do in this situation," Sophie continued. "It's something you aren't ever given a lesson on how to handle, especially when it's all happening in the public eye. So bare with me and know that I am grateful for all the love."
Days before his death, Sophie was in Malawi, where she was volunteering in various communities. She cut her trip short when she learned of his stroke.
"A lot has happened in the past week for me. Everything is happening so fast. I made it back from Malawi just in time to be here with my family," she said.
Our thoughts are prayers are with Perry's family.
Watch below... Remembering Luke Perry: a look back at his visit to Australia: