"I think I said I loved her and I appreciated her," Comer told ET's Kevin Frazier backstage, revealing what she whispered to Oh on her way to the stage. "Because honestly, this whole experience we've gone through together."
"We believed in the show, but we had no idea how humongous it was going to turn out to be. And to kind of have gone through it with her, she's been extremely generous on the screen, so I'm very, very grateful of her," she added.
The 26-year-old actress was visible shocked to have won over Oh, Emilia Clarke, Viola Davis, Laura Linney, Mandy Moore and Robin Wright in the category. "I just didn't expect it," she admitted. "The women in that category are so phenomenal, and I felt very lucky to be there and be here."
Comer thought her win was such a long shot that she told her parents not to come to the awards show with her. "I kind of was just like, 'Oh guys, this isn't the time. I don't want you to come and get your hopes up,'" she explained. "I just spoke to them. They just said they love me and they were extremely proud of me. So, that was nice."
"It's also, like, 6 a.m. or something in the U.K., so they're probably so drunk right now," Comer joked. "There wasn't much stringing of sentences together."
While her parents celebrate across the pond, Comer will enjoy the night with Oh and Phoebe Waller-Bridge (who served as showrunner on Killing Eve's first season, but nearly swept the Emmys with her series, Fleabag).
"I knew [Killing Eve] was special because of Phoebe. Phoebe is so, so incredible. But it is crazy. I never dreamed that I would be in this position at all," Comer said. "I don't know [where I'll put my Emmy]. I'm going to have to keep her safe... can't lose her!"
Emerald Fennell took over as showrunner for season two of Killing Eve, while Suzanne Heathcote has taken on the role for season three, which is currently filming.
"We have a new writer, Suzanne Heathcote, who is fabulous, and we still have the same tone of the show and everything that the show stands for," Comer told reporters backstage. "But there's a lot of craziness going on in London. I hope the viewers enjoy it. It's exciting."