He also took a swipe at media moguls, who he said kept nationalist governments in power.
Succession centres around character Logan Roy who runs much of the media in the United States. The character head of a dysfunctional family dynasty, played by actor Brian Cox, is said to be based on Rupert Murdoch.
Speaking from a hotel room in London, Mr Armstrong, who was brought up in Oswestry, thanked the judges for the award, the second year running Succession has taken the title.
“This is such a very nice moment but I am very sad not be be with the cast and some of the crew to share it,” he said.
He went on to say that he wanted to make a series of “un-thank yous” for being robbed of the opportunity to spend the night with peers.
“Un-thank you to the virus, for keeping us all apart this year,” he said.
“Un-thank you to President Trump for his crummy and uncoordinated response. Un-thank you to Boris Johnson and his government for doing the same in my country.”
“Un-thank you to all the nationalists and sort of quasi-nationalist governments in the world who are exactly the opposite of what we need right now. And un-thank you to the media moguls who do so much to keep them in power.”
Mr Armstrong began his rise to fame with his work on the Peep Show and Fresh Meat.
He then went on to create Succession. Sunday’s awards also saw him pick up the award for Writing for a Drama Series. Jeremy Strong, who plays Logan’s son Kendall, won an Emmy for the Outstanding Lead Actor in a drama series.
His speech saw Mr Armstrong speaking from a single chair, flanked behind by four socially distanced friends and colleagues. As if to strengthen his comic touch in his writing his speech was interrupted by a phone call in the hotel room, which one of his friends had to get up to answer.
“Not the time for room service,” Mr Armstrong joked.
The writer went to the University of Manchester after school in Oswestry and it was there that he met Peep Show co-writer Sam Bain.
His writing credits also include In the Loop, The Thick of It, and the film Four Lions.
He has also written a book, Love, Sex and other Foreign Policy Goals, which is set in Chirk and north Shropshire.
He was a supporter of Oswestry’s Literary Festival, attending the event for a question and answer session in 2016.