The Ukrainian knocked out the 22-time Grand Slam winner in the third round of the Games, beating her 6-4, 6-3 before falling 6-2, 6-0 by Petra Kvitova.
However, the 22-year-old, who has enjoyed her most successful year on the WTA to date, said the full extent of her achievements did not sink in until afterwards.
"It wasn't really a dream but a big challenge," Svitolina said during All-Access Hour at the VTB Kremlin Cup.
"Maybe subconsciously, I thought it to be impossible. When Serena plays at her best level, it's impossible to beat her. I didn't really think about it. The fact that it happened during the Olympics... I played very well that day, it was unexpected.
"Maybe she didn't expect me to play that well, and she said she was very surprised and congratulated me. For a player it's important to defeat your opponent but also to play well. I didn't make many unforced errors and attacked every ball. I think that's what she meant.
"I tried not to think about it because I had to play a match the next day but it was cancelled due to rain. Maybe after the tournament I tried not to be upset because defeating her was quite a big achievement.
"I understood that I made something for my country. Playing for the country is always a pleasure because your country supports you. But I couldn't win a medal."
Svitolina also defeated Angelique Kerber after the German usurped Williams as WTA World No.1, beating Kerber 6-3, 7-5 at the China Open. Despite being the only player this season with wins over both reigning No.1s, Svitolina says she has no tips for beating the best players in the world.
"I don't have any secrets. We had some tough matches. I won the first set pretty easily and served twice for the match. It was an important match for me because if I play at my best, we play with her at a quite same level.
"That win was not a win against the No.1 but against Angelique Kerber. If she gives an opportunity, I can beat her. She had an amazing year winning two Grand Slams, it's unbelievable. In the beginning of the year not a lot of people thought she could manage it.
"But she did and became No.1. It's an unbelievable achievement."
"The beginning was not so well. In Australia I lost a match to Osaka and it was painful and then I got injured. I couldn't play at 100 per cent. Then it was better. I felt better, both health- and game-wise. I came back to a stable level and the results followed. It was a transitional season. I changed my game and I think in the end of the year played well. I still have to play here and in Zhuhai."
Svitolina believes that some of her success has come as a result of the close working relationship she has with Justine Henin.
"It's a priceless experience for me. I guess what we achieved was over my expectations. It's good that she shares her moments on court," she explained.
"She shared what she felt when she played the finals of Grand Slams. I am not here yet. But it very interesting. And she could tell me what were the mistakes she made back then so that I don't repeat them. We changed some moments in the preparations and practices. I guess it became more professional."