In an exclusive interview with PEOPLE, the actress, 41, reveals her reaction when she first saw her former This Is Us costar's PEOPLE cover story, which hit newsstands last month.
"It just made my day," Moore -- who has partnered with anti-RSV medication Beyfortus -- says. "I opened up my phone and the first thing I saw was her gorgeous face on the cover of PEOPLE Magazine."
"Nobody deserves it more," continues the mother of three of Metz, 44. "Chrissy is such a hard worker. She's so gifted, she's such a talent, and being able to see her shine in every medium, whether it's music or on the big screen or small screen, she truly, truly deserves it."
Moore and Metz played mother and daughter, Rebecca Pearson and Kate Pearson, respectively, on This Is Us.
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In her PEOPLE cover story, Metz spoke candidly about her new life in Nashville, taking control of her health and being newly in love and in a supportive relationship.
Metz also discussed being a part of The Hunting Wives, a Netflix murder mystery series also starring Brittany Snow, Malin Akerman, Dermot Mulroney, Katie Lowes and more.
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When asked if she has tuned in to her former costar's series, which became a megahit over the summer, Moore admits, "I haven't watched it yet."
"But I'm so thrilled, and I miss her so much," she continues of Metz, adding, "I wish I got to see her as much as we all used to. But such is life."
Alongside Moore and Metz, This Is Us also starred Milo Ventimiglia, Sterling K. Brown, Justin Hartley, Susan Kelechi Watson, Chris Sullivan and more.
The series, which ran from September 2016 to May 2022, followed the Pearsons and all the ups and downs they went through as a family over the years.