Grainger was appointed as Wales boss in March 2021, becoming the country’s first ever full-time manager solely dedicated to just the women’s senior team.
She signed a new four-year deal in January 2023 after reaching the World Cup play-off final.
“I was approached by Norway and things happened very quickly,” added Grainger.
“It wasn’t expected for me, it was a surprise and sometimes the timing of how things are is not always perfect.
“I don’t think there ever would have been a perfect time for me to leave Wales, I certainly didn’t plan to leave at the time that I did and also at the speed that I did as well.
“But I felt like the opportunity that had been put in front of me was the right one for me to take.
“I knew the players were upset, I knew they would be upset with me leaving at that time as well.
“I do believe in the journey, I do believe in the team, that’s still what I believe in.
“I still follow the team closely, I’m still very close to the team but it was a decision that I had to make and my only hope was that the players would understand.
“Everyone in football gets opportunities at different times, them as players when they move to different clubs.
“It didn’t mean that what I said about believing in the journey and believing in the team wasn’t true, it was just something that I felt was the right thing to do for me.”