Maria Sharapova's Grand Slam return after a 15-month doping ban ended in defeat Sunday at the US Open but the former world number one considered it a major step in her comeback.
"She played unbelievable throughout the first and second set and I just kept fighting, running for every ball," Sevastova said. "I had to stay pumped up and run and make her work for every point.
"I was confident. I was feeling it. But still you have to beat her. She was playing one of the best matches here."
Sharapova returned from her suspension in April, was snubbed for a French Open wildcard and missed Wimbledon with a thigh injury but received a US Open wildcard despite only one hardcourt tuneup match due to a left forearm injury.
"It's great to get that major out of the way," Sharapova said. "I'm thankful for the opportunity. I did my best and I can be proud of that."
US ninth seed Venus Williams, a seven-time Grand Slam champion, advanced by defeating Spain's 35th-ranked Carla Suarez Navarro 6-3, 3-6, 6-1.
The Wimbledon and Australian Open runner-up, seeking her third US Open crown, will meet the winner of a later match between Wimbledon champion Garbine Muguruza, the third seed from Spain, and Czech 13th seed Petra Kvitova, a two-time Wimbledon winner.
"I'm focused on myself and trying to be as aggressive as possible," Williams said.
"Nobody ever gives you a Slam. You've got to take it and I'm going to try and take it."
Stephens, who was a 2013 Australian Open semi-finalist, missed 11 months with a foot injury that required surgery in January and returned only at Wimbledon, but has won 12 of her past 14 matches for her deepest US Open run in six tries.
"I honestly couldn't have asked for a better comeback," Stephens said. "Making it to the quarter-finals here is unbelievable."