Stanley Tucci's first wife, Kate Tucci, died of breast cancer in 2009

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Stanley Tucci is reflecting on the death of his first wife, Kate Tucci.

In a new interview with CBS Sunday Morning's Holly Williams, the 60-year-old actor said he still grieves the loss of Kate, who died in 2009 of breast cancer at age 47.

"You never stop grieving," said Tucci, who shares twins Nicolo and Isabel, 21, and daughter Camilla, 19, with Kate.

"It's still hard after 11 years," he added. "It's still hard. And it will always be hard. But you can't let it... and she would never want any of us to ever wallow in that grief and let it take over our lives. She would never want that. She wasn't like that."

The Supernova star was married to Kate from 1995 until her death in 2009.

He wed Felicity Blunt, an English literary agent and the older sister of actress Emily Blunt, in 2012. Tucci and his second wife welcomed two children: 6-year-old son Matteo Oliver, and 2-year-old daughter Emilia Giovanna.

Kate and Stanley Tucci
Kate and Stanley Tucci

Tucci previously spoke about the death of his first wife in an interview with NPR in 2010, just one year after her death.

"There's all the blaming of yourself, which you can't do, but you kind of do," he shared at the time, "and I'm just — I'm mostly sad."

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Amid the coronavirus lockdown, Tucci, who has been in the U.K. with his family, became a sensation thanks to his cocktail-making skills.

Last April, Tucci went viral on Instagram for his charming how-to video tutorial creating his homemade Negronis, which his wife Felicity first suggested he do.

And along with helping Tucci's video reach over 1 million views, his followers also had some very enthusiastic responses to share.

"Surprised isn't the word. I'm shocked and appalled," Tucci joked to PEOPLE in a recent interview. "I'm so flattered. We had no idea."

Stanley Tucci
Stanley Tucci
| Credit: CBS via Getty

The Hunger Games actor, a known cocktail enthusiast among his peers and costars, explained how it was Felicity's idea to start doing the Negroni demos at home.

"She said, 'Would you do a little cocktail thing, just for the Curtis-Brown people? It would be fun, cheer people up,' " he recalled. "So I did. And then she said, 'Well, maybe put it on your Instagram.' And then the world changed."

Tucci said that he could not believe the creatives responses that fans had for his demo videos.

"I mean, some of them were so funny. Filthy, but funny," he said. "We laughed so hard, reading them out loud. And they were great, like very flattering too, like really flattering."