The series, which aired on BBC Two in the UK and Showtime in the US earlier this year, stars Greig and Stephen Mangan as two writers who begin working on an American remake of their hit British show.
"The BBC and Showtime did a very clever thing in calling it 'Matt LeBlanc's comedy'," Greig told The Daily Telegraph.
"I don't actually think it is a comedy. I think it's a drama that is very realistic and has funny bits in it. The two characters are based on the writers of the show - David Crane says he looks at life and thinks the glass is half full. Jeffrey [Klarik] looks at life and thinks the glass is an idiot."
Greig also confessed that she is always surprised by the attention her co-star Matt LeBlanc attracts.
"I've been so amazed at the number of really professional top-of-their-game women who I know to be intelligent, well-educated and brilliant who have said, 'What was it like to snog Matt LeBlanc?'" she joked. "He is extraordinary. And my children absolutely adore him. That's not to belittle him. He can turn on a sixpence. He can smell a joke a mile off."
Episodes was renewed for a second season in February. Greig will also film new episodes of her Channel 4 show Friday Night Dinner.