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Michael Keaton, Andrew Garfield and Jessica Chastain were also among those to throw the spotlight to the war that is taking place following the Russian invasion, hailing the strength of Ukrainian president Volodymyr Zelenskyy, who is a former comedian and actor.
House of Gucci star Lady Gaga said on the red carpet: "This is a beautiful night where we all get to celebrate art together and celebrate each other. There's so much going on in the world and my heart goes out to Ukraine. I think tonight we should all really sit in the gratitude of this."
Michael Douglas, 77, pointed to a blue-and-yellow pocket square he wore to resemble the Ukrainian flag, and said: "This is not the LA Rams [football team].
"If ever there was a time for us to appreciate what true democracy is, I'm just so proud of what these people of this country have done."
Succession star Cox, 75, took the chance to pay tribute to the Ukraine as he accepted the Outstanding Performance by an Ensemble award for the hit HBO show.
He said: "This is a thing that's come to me about what's going on in the Ukraine. It's truly, truly awful, really, really awful what's happening. And it's particularly awful in terms of what is affecting the other people, particularly in our profession.
Watch: Brian Cox praises Ukrainian president
"The thing that's really distressed me is what's happening in Russia to my fellow actors and actresses and performers, and critics.
"They are told under pain of high treason that they cannot say a word about Ukraine. And I think that is pretty awful.
"I think we should all stand together and also for those people in Russia who do not like what's going on, particularly the artists."
Cox added: "The president of Ukraine was a comic, you know, he was a wonderful comic performer.
"And we should respect that for him, and to come to the presidency is amazing."
Michael Keaton also paid tribute to the Ukrainian president while accepted the award for best male actor in a miniseries or TV movie for Dopesick.
He said: 'We have a fellow actor in Zelenskyy, who deserves some credit tonight for fighting the fight."
Spider-Man star Andrew Garfield admitted on the red carpet that it felt "weird" to be celebrating, knowing what was happening in Ukraine.
He said: "It's a tricky day to celebrate. Keeping what's happening in Ukraine in our hearts. It's weird."
And accepting the award for female actor in a film for The Eyes of Tammy Faye, Jessica Chastain said: "My heart is with our international family all over the world right now, who is fighting for their safety and their freedom."
Russian president Vladimir Putin began an invasion of Ukraine on 24 February.