Sandra Harwitt of USA Today provided comments from the 23-time Grand Slam singles champion, who called the 18-year-old Ukrainian "a good talent."
"As she was walking towards the net, I could tell she was quite upset," Williams said. "I kind of liked that. It shows she wasn't just there to play a good match; she was there to win. She wanted to win. That really broke my heart."
The 37-year-old American was dominant in every facet of the third-round match. She racked up eight aces, won 84.6 percent of the points on her first serve and converted five of her 12 break opportunities, while Yastremska didn't generate any break points.
The rising star—who defeated Samantha Stosur and Carla Suarez Navarro to reach Round 3—sounded upbeat in a later Instagram post.
"Learned here in AO a great lesson for the future to come," she wrote. "The season has just started!"
Williams advanced to a star-studded clash with top-seeded Simona Halep in the fourth round.
Halep defeated Serena's sister Venus 6-2, 6-3 in one of Saturday's other matches in Australia.