After starting the day four strokes back from third-round leader Brittany Lincicome, Ko made a concerted charge for the crown but bogeys at 17 and 18 saw her settle for a two-under 70 in her final round as she finished the tournament at eight-under.
Lincicome then lost to Inbee Park in a playoff after the pair finished at 11-under. It was Park's fifth major title.
"It was kind of disappointing finishing with two bogeys, but overall I played pretty solid today, and I tried to give myself opportunities, and made a lot of good putts," Ko told reporters after her final round.
"So yeah, I'm pretty happy with how the major has finished."
Ko's third-place finish was her best of the year in a major and the second-best of her career, after her efforts at the Evian in 2013.
"This gives me a lot of confidence," Ko said.
"You know, majors are, I guess, where we try and perform our best, and to have a top-five finish, that's really good. Yeah, so I'm excited for next week, and I've got a lot of confidence from this week."
Ko could have climbed to No1 in the world if she had won in New York but a major maiden title and the world's top billing don't seem far off for the laid-back kid from the North Shore who is rarely flustered.
"Obviously I do get nervous at some points, but you know, I just try and go out and have some fun, and if it goes my way, great.
"If it doesn't, I can't do much about it."
Ko, who is certain to be named Rookie of the Year on the LPGA Tour, will head to Canada this week looking to continue her remarkable run at the Canadian Open, which she won back-to-back as an amateur in 2012 and 2013.