The 22-year-old, from Wales, was leading 21-15 with fewer than 15 seconds remaining but European champion Jelic mounted a stunning late comeback to deny Williams the gold on her Olympic debut and emulate her victory against the Welshwoman in the European Championships in Sofia earlier this year,
Williams, who lived in a caravan while training, was guaranteed a medal by reaching the final and walks away with silver after Jelic posted a 25-22 victory.
Speaking to BBC Sport after the match, Williams was pragmatic: “I know it’s not enough. I had her, ten seconds… I messed up, I made a mistake. So it’s on me.
"I couldn’t do much about it. I didn’t go out there to lose, I went out there to win. I was pretty confident, I tried my best in that situation but it just didn’t happen on the day.
"I’m very happy with how I performed, it’s just a shame she got in the last ten – but an Olympic silver medal’s not bad, is it?”
Williams endured a less-than-ideal start to the Tokyo 2020 Olympics, dealing first with injury and then a late arrival in Japan.
She added: “I’ve not had the best prep but that's not an excuse; I felt good coming into today.
"It’s been absolutely crazy, for my first Olympic Games – a very good experience.”
Egypt’s Hedaya Malak took bronze for a second successive Games after seeing off Paige McPherson of the USA in their medal bout.