The Scottish actress was cast in the hit drama's original pilot as Jessica Brody, but was replaced by Morena Baccarin when the show was picked up to series.
"I mean, I know that happens - people get replaced - but I was really sad to leave that part because I loved that part," Fraser admitted to Vulture. "I made peace with it.
"You can't take these things personally, even though you do for a couple days. You're like, 'Ahhh, it hurts'. But you know, it's just one of these things in the industry that you have to deal with sometimes."
The 36-year-old was later cast on Breaking Bad, playing Lydia Rodarte-Quayle on the AMC drama's current fifth season.
"If I hadn't had lost that [role on Homeland], I wouldn't have got this wonderful role," she explained. "So I'm actually just super happy. Lydia is a f**king awesome role and I just feel incredibly fortunate."
Breaking Bad continues on Sunday nights on AMC, while Homeland will return to Showtime in the US and Channel 4 in the UK later this year.