Martin Short has spoken for the first time about the death of his daughter, Katherine Short, saying her death has been “a nightmare for the family”.

Katherine died in February aged 42, at her home in the Hollywood Hills. The County of Los Angeles Medical Examiner’s office confirmed she died by suicide.

Speaking on CBS News Sunday Morning, the 76-year-old comedian and actor compared his daughter’s death with that of his wife, Nancy Dolman, who died of ovarian cancer in 2010 aged 58.

“The understanding [is] that mental health and cancer, like my wife’s, are both diseases, and sometimes with diseases they are terminal,” Short said. “And my daughter fought for a long time with extreme mental health, borderline personality disorder, other things, and did the best she could, until she couldn’t.

“So, Nan’s last words to me were, ‘Martin, let me go.’ And what [Katherine] was just saying [was], ‘Dad, let me go.’”

Short said he had a “deep desire” to take “mental health out of the shadows” so people wouldn’t be “ashamed” of talking about it.

“Not hiding from the word suicide, but accepting that this can be the last stage of an illness,” he said.

Short also spoke of losing several close friends and family in the past year, including his sister-in-law, his daughter and his friends Diane Keaton, Rob and Michele Reiner and Catherine O’Hara.

“It’s staggering,” he said, adding: “You just have to breathe in, breathe out.”

Katherine was the eldest of three children adopted by Short and Dolman. She largely kept out of the spotlight, though she sometimes attended events and walked red carpets with her father. She received a bachelor’s degree in psychology and gender sexuality studies from New York University in 2006, as well as a master’s in social work from the University of Southern California in 2010, and went on to work in private practice as a licensed clinical social worker.

Short has previously spoken about losing Dolman, telling the Guardian in 2012: “This is the thing of life that we live in denial about, that it will ever happen to us or our loved ones, and when it does you gain a little and you suffer a little. There’s no big surprise.”

Martin spoke to CBS ahead of a new Netflix documentary film about his life titled Marty, Life Is Short, which premieres 12 May. The documentary touches on Short’s many experiences with loss early in life: his older brother David was killed in a car accident when Short was 12, and both of his parents died when he was still a teenager.

Short said this led to him developing “this muscle of survival and handling grief and a perspective on it”, as well as the bravery to become a performer: “I think if you’ve gone through that, an audience not liking you is really not that important any more.”

• In the US, you can call or text the 988 Suicide & Crisis Lifeline at 988 or chat at 988lifeline.org. In the UK and Ireland, Samaritans can be contacted on freephone 116 123, or email jo@samaritans.org or jo@samaritans.ie. In Australia, the crisis support service Lifeline is 13 11 14. Other international helplines can be found at befrienders.org