The second-round loss comes on the back of her heaviest career defeat, a 6-1 6-0 loss to Britain's Johanna Konta in the Silicon Valley Classic first round.
"I'm still at the very beginning," said the 23-time Grand Slam champion.
"I'm just going to continue to work hard, and hopefully I'll start winning more matches."
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Following the thumping by Konta, the 36-year-old American, runner-up at this year's Wimbledon, withdrew from last week's Rogers Cup in Canada for "personal reasons". She later clarified that she had been struggling with post-natal emotions.
The two-time Cincinnati champion, who only returned to the women's tour earlier this year after giving birth, looked impressive in her opening match at the Western & Southern Open as she fired down eight aces en route to a 6-1 6-2 win over Australian world number 23 Daria Gavrilova.
And after losing the first set to two-time Wimbledon champion Kvitova, Williams showed similar form as she levelled the match. Both players broke serve at the start of the third set, before the eighth seed broke again at 4-2 and then held serve to progress to the third round.
"It was a pleasure to share the court with Serena, she's such a champion," said Kvitova. "We are both coming back - from injury, from motherhood - so it's something really special to play her."