The 20-year-old's mom, Dianna De La Garza, also tweeted, "Thank you for the outpouring of love and prayers. Y'all are amazing!"
The X Factor judge has yet to comment on her father's death, whom she shared a tumultuous relationship with and who was the subject of her 2011 song, "For the Love of a Daughter" from her Unbroken album.
In 2010, when the former Disney star was seeking treatment for emotional and physical issues, her estranged father spoke out to the press, trying to reach the singer/actress, much to the teen's dismay.
A year before that, in 2009, the star spoke to New York Daily News about the situation involving her father, saying, "The last time I talked to him was two years ago. You try to have faith in somebody, even when you're the last person that believes in him. But when somebody lets you down after you've been the only one there for them, and so many times, you don't know what else to do."
She later added, "I had to cut off all connection. It was hurting me too much."
While talking to Radar Online in October 2011, Patrick, who was living in New Mexico at the time, told the site he was ailing from cancer and trying to get through to his daughter. “It is not like I want anything from her, all I want is her love,” he said.