The top seed sealed a 6-3 6-3 victory over Kaia Kanepi of Estonia at Flushing Meadows to progress to the last eight after a largely disappointing season.
Now I’m more relaxed. I feel like I don’t have to win any more.
Williams said: “I never thought it [reaching the quarter-finals] would be so exciting (smiling). It feels good.
“Obviously I don’t want this to end. But I’m just happy that I’m able to be performing a little better at the end of the year.”
The 32-year-old went on to reveal that she feels more “relaxed” as she approaches the twilight years of her career.
“I’m a perfectionist, I always want to be the best, do the best,” she continued.
“I think I put a lot of pressure on myself to do well, particularly in the Slams, to do really well.
“I had a couple nagging injuries that definitely didn’t help. But other than that it was just that.
“Now I’m more relaxed. I feel like I don’t have to win any more. I’ve had a wonderful career. Tennis has given me so much, things I would have never expected in my life.
“I feel honoured to even be a part of such a wonderful sport. So I think ultimately that really helps me to be able to be more relaxed.”
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