"He was so sweet," Parsons told PEOPLE after Stonestreet promised his mom she could take his trophy home. But Parsons couldn't quite muster the courage to follow that magnanimous gesture.
"My mother will not be getting this Emmy," he said with a smile. "She can visit it."
Stonestreet, 38, who based his Modern Family character, Cameron, partly on his mother Jamie, was able to thank her in person – she was in the audience on Sunday.
Parsons, who won for his work as Sheldon Cooper on The Big Bang Theory, called his mom while on his way to the Governors Ball after the show – and found her very emotional. "My mother sounded very good, but [she was] still crying, which was really sweet," he says. "And it was over two hours since it had happened, so I hope she's okay."
Parsons said the whole night was surreal, particularly the moment his name was called and he walked up to accept the award. "I felt like, 'This could be a dream,' " he said.
He added that he doesn't have a special place in mind for where to keep the trophy. But he has a few ideas. "I have a bookcase," he said. "I also play the piano. I could put it on top of a piano. Is that odd?"