Wales coach Warren Gatland feared Williams had suffered a recurrence of the metatarsal injury which forced him to undergo surgery in June and had made him a doubt for the tournament.
"We are very sorry," kicking coach Neil Jenkins told reporters on Sunday.
"He has been an outstanding player for us and he came back from an injury too. He is a huge loss but we have had quite a few of them so far. So we just have to get on with it."
Williams played in the opening match against Uruguay but sustained a concussion against England and missed the third pool match with Fiji.
Jenkins said discussions on who would replace the versatile back had not yet started.
Wales have been dogged by a succession of injuries but still finished runners-up in Pool A and will face South Africa in the quarter-finals next Saturday.
Williams came in at fullback after Leigh Halfpenny was injured in their final warm-up match, joining a casualty list that also includes centres Jonathan Davies and Scott Williams, scrumhalf Rhys Webb and winger Hallam Amos.
"I didn't imagine so many," Jenkins added. "(But) the players that have come in have done exceptionally well. It is what it is. It's an opportunity for the players coming in.
"(Scrumhalf) Gareth (Davies) has done that and played exceptionally well. We prepared as best as we could with the wider training squad. We have had incredible bad luck.
"We have got to go again next week against an incredibly physical side in South Africa."
The loss to Australia in an energy-sapping, tryless contest at Twickenham on Saturday ensured that rather than play Scotland in the quarter-finals next weekend, Gatland's side will take on the Springboks.
"The game was incredibly close, especially at 12-6," said former flyhalf Jenkins.
"We couldn't quite get the ball down. It was fantastic defence from Australia's perspective. We wanted to go through as group winners but it didn't quite go our way."
The Welsh beat South Africa 12-6 in their last meeting in Cardiff a year ago but that was one of only two victories in 30 tests against the southern hemisphere powerhouse.
(Reporting by Justin Palmer and Nick Mulvenney,; Editing by Ed Osmond)
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