The actor wasn't at the ceremony to accept the award, but remembered Williams in a statement posted to Twitter on Monday.
Menzies, who starred as Prince Philip on the Netflix drama about the royal family, earned the Emmy on Sunday for Outstanding Supporting Actor in a Drama Series -- the same category in which Williams was nominated for his performance on Lovecraft Country.
Menzies was unable to attend the ceremony, but shared his thanks on Monday, and honored Williams with a nod to one of the late actor's most iconic roles.
"Very humbled to win @TheEmmys last night, huge thanks to @TVAcademy & congrats to all my brilliant fellow nominees," Menzies wrote. "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."
This was Menzies' first win, as well as his first nomination. Meanwhile, it was Williams' fifth nomination in total.
While Williams was not awarded the Emmy, his absence was felt and his memory honored at this year's awards. Several stars paid tribute to him during acceptance speeches and presentations, and he was honored with a special moment during this year's In Memoriam segment.
See the video below for more on how some stars honored Williams' life and legacy at this year's Emmy Awards.