Williams, 36, walked away from the 2016 Olympic Games with a silver medal, but the win was bittersweet after she and her 34-year-old sister, Serena, were defeated during the first round of the women's doubles tournament.
"We played one match," Williams tells PEOPLE. "It was one of those days where nothing went right for us and our opponents were on fire."
She added: "Sometimes that happens and you hope it doesn't happen at the Olympics and it's not like you get another chance next week or, 'Hey, in three months we're playing again.' It's like, 'Okay, wait four years.' "
The three-time gold medalists – the sisters won gold in 2000, 2008 and 2012 – were expected to win a fourth time, but the Czech team of Lucie Safarova and Barbora Strycova came out the victors, beating the Williams' 6-3,6-4.
"When you play there you have to figure out how to win if it's not your best day," Williams tells PEOPLE. "We couldn't do it that day, but we're still grateful for all the other experiences."
The Olympics didn't end in total disappointment for Williams, though. The tennis great took home a silver medal in the mixed doubles gold medal match – a win she calls "amazing."
"We were very close to gold, but I know that the match that I played was really a gold-medal level," she says of the match played with Rajeev Ram. "I felt amazing about my performance out there on the court and that was the best part."
She adds: "So, I could walk away feeling like, 'Oh my gosh, I gave my all, gave it more than my all.' It feels good to leave an Olympics on that level."
Her little sister did not fare as well. Serena was knocked out of the Rio Olympics entirely after losing in a third round singles match to Ukraine's Elina Svitolina."
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