In a nail-biting close final, Valerie led after throwing a massive 20.42m on her second attempt.
Her effort put her streets ahead of her competitors, until Carter stepped up and threw her unbeatable 20.63m.
Valerie had a chance to take back the lead but her final throw saw a landing of 20.39m.
Already a double Olympic champion, Valerie had set her sights on becoming the first woman to win three gold medals for her sport.
So far, no New Zealand athlete has claimed three consecutive Olympic gold medals.
After the final, Valerie told Sky Sports she was not too disappointed.
“I am ok – it would have been nice to win, that was the whole goal, but that’s sport,” she told Sky Sports.
"I came out here and left my heart out here and I fought to the very end and after where I was last year to now, I've done a lot of work to be here today and I'm very blessed to be here today.
"It is my third Olympic medal and I've got to take it and run."