In the first public statement since he died of a suspected overdose last week, Grande described him as her "dearest friend" and the "kindest, sweetest soul with demons he never deserved".
In the caption of a video, she said she was "so sorry" she hadn't been able to fix or take his pain away.
Miller, real name Malcolm McCormick, was open about his drug abuse.
He was found dead at his home in California. The official cause of death has not yet been announced.