updated 03/15/2013 AT 4:00 PM ET
•originally published 03/15/2013 AT 2:30 PM ET
“She’s precious,” he tells PEOPLE. “One gaze into those beautiful blue eyes of hers, and she’s got you.”
The actor met the feline during his visit to the South by Southwest festival last weekend, where he participated in a Mashable interview, and admits he had a hard time letting her go.
And it turns out the former Lost star wasn’t the only person left mesmerized by the encounter.
“The mom gave me a card and it’s a picture of her smiling. She wrote her number on it,” he says. “She said, ‘If you want to see Grumpy Cat, call me.’ Grumpy Cat is a wing woman.”