Alexa Ray Joel was hospitalised last December after taking eight pills of Traumeel, a homeopathic ibuprofen substitute.
The 55-year-old told Ladies' Home Journal: "Your job as a parent is to listen. And to dole out as much love as you can. That includes tough love. I told Alexa, 'You got yourself worked into such a tizzy. You need to examine that, you need to seek professional advice'.
"She tried to do something dramatic to prove to her boyfriend how much he hurt her. I think many people can relate to that excruciating pain of love gone wrong. I'd rather have a broken arm than a broken heart."
Brinkley also insisted that her daughter wasn't attempting suicide and that she has decided to take time to focus on her career.