Menzies, 47, took home the award for outstanding supporting actor in a drama series at the 73rd Primetime Emmy Awards on Sunday night for his role as Prince Philip, Duke of Edinburgh, in Netflix's The Crown.
On Monday, Menzies — who was not present at the show to accept the award — wrote that he was "very humbled" by the win but that he wanted to "dedicate" the honor to Williams, who was also nominated in the category for his role in Lovecraft Country.
"His performance as Omar in The Wire is one of the great screen performances, he will be deeply missed. RIP," he concluded his tweet.
Very humbled to win @TheEmmys last night, huge thanks to @TVAcademy & congrats to all my brilliant fellow nominees. But want to dedicate this to Michael K Williams, his performance as Omar in The Wire is one of the great screen performances, he will be deeply missed. RIP🙏
— Tobias Menzies (@TobiasMenzies) September 20, 2021
Williams was found dead at age 54 on Sept. 6 in his Brooklyn penthouse apartment, a source from the NYPD told PEOPLE at the time. Williams' nephew discovered his body in the living room.
Prior to presenting the award for outstanding supporting actor in a drama series on Sunday, Kerry Washington paid tribute to Williams, whose death occurred after the voting period for the 2021 Emmys.
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"The nominees for this next award astounded us with each of their uniquely remarkable, memorable performances this past year. But I would like to take a moment to mention one nominee in particular, Michael K. Williams," Washington began her presentation. "Michael was — it's crazy to say Michael was — a brilliantly talented actor and a generous human being who has left us far too soon."
RELATED VIDEO: Kerry Washington Pays Tribute to Late Michael K. Williams at 2021 Emmys: 'Left Us Far Too Soon'
"Michael, I know you're here because you wouldn't miss this. Your excellence, your artistry will endure, we love you," she concluded.
Washington appeared with Williams in the 2007 film I Think I Love My Wife as well as Spike Lee's 2008 movie Miracle at St. Anna. The actress honored Williams earlier this month with a heartfelt Instagram tribute.
"So heartbroken. @bkbmg thank you for the beauty and joy you brought to the world. Sending love and prayers to your friends, family and everyone who adored you 🙏🏾 me included ❤️ We adore you Sir," she captioned the post.