The 48-year-old English actress broke her silence in an interview with The Daily Telegraph Australia after separating from Schreiber after two children and 11 years together.
"I feel I'm in a good place in my life and I want to make sure my kids are healthy, my kids are happy and things are going to go well," Watts said. "Those are my hopes for me and for all of us."
"I feel, whether you're famous or not, transitions are scary for anybody," she later added. "I feel like change is always scary, but that's only because transition for anyone is new and you wonder how things are going to go."
Watts and Schreiber have co-starred in several movies, including The Painted Veil and The Bleeder, and share two sons, 9-year-old Alexander and 7-year-old Samuel. The couple announced their split in a joint statement in September.
"Over the past few months we've come to the conclusion that the best way forward for us as a family is to separate as a couple," the pair said.
"It is with great love, respect, and friendship in our hearts that we look forward to raising our children together and exploring this new phase of our relationship," they added. "While we appreciate your curiosity and support, we ask the press be mindful of our children and respect their right to privacy."
Watts showed her support for Schreiber in October by attending the opening of his Broadway play Les Liasons Dangereuses. She will star on the new Netflix series Gypsy and also appear in Showtime's revival of Twin Peaks.