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"Me, being here by myself, I cannot believe I'm here ... let me pull myself together," she said, before thanking the Academy.
The film, as well as Youn, have received critical acclaim throughout awards season, with Youn winning a Screen Actors Guild Award and a BAFTA before her Oscar win.
She explained how frequently her name has been mispronounced throughout her travels and said, "tonight you are all forgiven."
Youn also acknowledged her fellow nominees in the category, Amanda Seyfried, Olivia Colman, Maria Bakalova and Glenn Close, who Youn said she has long admired.
"I don't believe in competition," Youn said.
Among her many charming moments on stage, Youn, who was presented the award by Brad Pitt, gushed a bit about their encounter.
"Mr. Brad Pitt, finally, nice to meet you!" she joked.