The American went toe-to-toe with the powerful second seed for 102 minutes on Thursday but was unable to replicate her victory in last year's US Open final and get a shot at landing a second major title as she went down 7-6(2), 6-4.
"Tough match for me tonight. Overall a positive tournament. I had chances in both sets, but she played better tonight," said Gauff. "I think it just came down to a couple of points, and that's tennis.
"At this stage in any tournament, but especially a Grand Slam, whether I lost 6-1 6-1, or like I did today, or in a third-set tiebreak, I still think it would hurt just as much."
Gauff said she thought she had played better in Thursday's clash than at Flushing Meadows last September when she clinched her first Grand Slam title in three sets.
The world number four made such a big impression on the sport's biggest stage at such a young age that it seems remarkable that her teens will only come to an end in March.
Although she was generally quite hard on herself, Gauff said she was proud of her achievements in the 4-1/2 years since she reached the fourth round of Wimbledon at the age of 15.
"Overall, this stage of my life, it was obviously a successful time," she added.
"I did want to win a Slam as a teenager, and I did that. Obviously today I was hoping to get number two, or at least give myself a chance to get number two.
"It didn't happen, but I feel like I'm there. So hopefully I can go only upwards from here."
Most importantly, perhaps, Gauff said she was still enjoying her tennis, even in defeat.
"I watched these matches growing up and watching Serena (Williams) and watching (Maria) Sharapova lose these matches," she said.
"When you're in it, it feels like the end of the world but then when you look at history, they didn't let one match define their career.
"I'm going to dwell on it tonight but... the sun is going to rise tomorrow. Tomorrow, I don't know, I'm going to try to go to the movies or something, be proud of myself."
