"She has a great serve. She does everything well. I think she's a good player," said Williams.
It was the first time the 20-year-old Frenchwoman had taken a set off Williams after two previous meetings last year.
"This time, I did a lot of work and I'm growing in my game and growing in my head, too," said Garcia. "It was a good match to play and a good test for me because she's a good player and she's always fighting a lot. I'm happy with what I did, but it's still disappointing because I didn't win."
Garcia burst on the scene by leading Maria Sharapova 6-3, 4-1 at the 2011 French Open, prompting Andy Murray to tweet that she looked like a potential No. 1:
The girl sharapova is playing is going to be number one in the world one day caroline garcia, what a player u heard it here first— Andy Murray (@andy_murray) May 26, 2011
The attention was disconcerting at the time, admitted Garcia.
"Everyone was talking to me about this, not my match or how I played -- just, ‘Murray says you will be No. 1.’ And I was like 150 in the world, so it was not easy when you’re 17 years old and you are like nowhere and someone says you will be No. 1."
"But I’m happy he said it because he knows tennis a lot, so it was good motivation for me," she added.
Garcia is ranked No. 74, just a few spots behind her high of No. 69.