She lost 6-4 6-3 to Svitolina, who currently ranks as number 20 in the world. Her struggles were highlighted by five double faults in the seventh game of the second set.
“It didn’t work out the way I wanted it to but at least I was able to make it to Rio – that was one of my goals,” she said afterwards.
“The better player today won but I know next time is going to be a really good match and I look forward to it.”
Svitolina, who will face the Czech Republic’s Petra Kvitova in the quarter-finals, said: “It’s an unreal feeling for me. This is just a perfect moment.”
Williams and her sister Venus were knocked out of the women’s doubles on Sunday by Czech Republic pair Lucie Safarova and Barbora Strycova.