01/16/2012 AT 09:00 AM EST
Peter Dinklage was a winner at Sunday's Golden Globes
, but he had other things on his mind while accepting.
After telling his fellow actors that he and wife Erica
left their new daughter with a babysitter for the first time, the Game of Thrones
star, 42, came backstage and told PEOPLE his nerves were calm about the situation – at least for the time being.
"Everything's fine – so far," Dinklage, 42, said, laughing. "She's a baby. Crying never killed anyone. Well, maybe that's not true."
The key to staying relaxed while being apart from his little one?
Dinklage joked, "It's all about the texting."