The late rocker's song "When Bad Does Good" earned him a Grammy in the best rock performance category
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Chris Cornell‘s two youngest children — Toni, 14, and son Christopher, 13 — accepted their father’s posthumous Grammy award on Sunday at the 61st annual honors, assuring the rocker’s legacy will live on after his death.

But taking the stage the Staples Center in Los Angeles to honor Cornell, who died by suicide in May 2017, wasn’t easy.

“It was very difficult,” Toni told reporters including PEOPLE backstage after the awards.

“We miss him so much and we saw him work on this so hard — he was always working on his music [because] it was his passion. It was really sad in a way to feel like he couldn’t be there himself to accept it for something that he was so proud of and worked so hard on.”

“We’re so proud of him,” she added. “It was amazing.”

Toni and Christopher Cornell
Toni and Christopher Cornell

Toni also noted that they were moved by the tribute concert for their father earlier this year, which featured performers and attendees including Miley Cyrus, Brad Pitt and Adam Levine. “I mean, it was amazing. I loved every single person who performed. It just really showed who he was and I love that.”

Added Christopher, “I agree with mostly everything she says. It was just beautiful to watch. The amazing people that came and helped perform – it was beautiful.”

Toni Cornell, Christopher Cornell, and Vicky Cornell
| Credit: John Shearer/Getty Images
61st Annual GRAMMY Awards - Arrivals
Toni Cornell and Christopher Cornell
| Credit: Amy Sussman/FilmMagic
61st Annual GRAMMY Awards - Red Carpet
Christopher Cornell, Vicky Cornell, and Toni Cornell
| Credit: Neilson Barnard/Getty

Both Toni and Christopher walked the Grammys red carpet together with mom Vicky Cornell (the late rocker was also a father to daughter Lily, 18). Toni paid homage to her dad by wearing a shirt with a photo of him on it.

Cornell was honored with a posthumous award in the best rock performance category for “When Bad Does Good.”

He wasn’t the only artist who has been nominated posthumously for an award. Mac Miller, who died in September, earned a nod in the best rap album category for his fifth studio album Swimmingthough lost the trophy to Cardi B, who later dedicated it to him.

Recording Academy President Neil Portnow told PEOPLE prior to announcing the nominees that their voting process makes it possible to honor artists that have recently died since they “are really looking at the music that gets made and released in any given year.”

“Sadly, sometimes we lose some of those artists for one reason or another,” Portnow, 70, said. “Sometimes, sadly, that is just going to happen.”

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Chris Cornell, wife Vicky, daughter Toni and son Christopher
| Credit: Paul Zimmerman/Getty

While Cornell’s death was ruled a suicide, his family has stated that they didn’t believe Cornell to be suicidal. Vicky said she believes that the side effects of the prescription drug Ativan — which can cause worsening depression and thoughts of self-harm in rare cases — may have impacted Cornell.

A month after his death, the rocker’s wife opened up to PEOPLE exclusively about her husband’s addiction and death.

“My Chris was happy, loving, caring and warm,” she said. “This was not a depressed man — it wasn’t like I missed that. What I missed were the signs of addiction.” Vicky believes that if her husband had not relapsed on drugs that night, he would not have died.

“He didn’t want to die,” she said of Cornell, who was prescribed Ativan as a sleep aid but doubled his dose the night of his death. “If he was of sound mind, I know he wouldn’t have done this… Addiction is a disease. That disease can take over you and has full power.”

If you or someone you know is considering suicide, please contact the National Suicide Prevention Lifeline at 1-800-273-TALK (8255), text “home” to the Crisis Text Line at 741-741 or go to