The Wallabies outscored Fiji by two tries to one, with Mark Nawaqanitawase and Suliasi Vunivalu scoring their five-pointers while Josua Tuisova dotted down for the Pacific Islanders.
Australia's discipline let them down badly, however, as they conceded a plethora of penalties, but Jones admitted that the buck stops with him after the loss.
"After that, I probably deserved more, mate," he said. "They should be throwing baguettes and croissants at me. I deserve whatever I get."
Australia coughed up 18 penalties to Fiji's seven during the match, with Simione Kuruvoli slotting four three-pointers off the kicking tee and Frank Lomani one, while Kuruvoli also converted Tuisova's try to finish with a 14-point contribution as Fiji sealed their first win over Australia since 1954.
Jones admitted afterwards that Fiji were deserved victors and highlighted the importance of their next match against Wales in Lyon on September 24.
"Well, thoroughly deserved victory for Fiji," he told ITV. "They outplayed us, particularly around the ruck.
"The turnovers they had, they executed three times more turnovers than us. In a close game like that, that was the difference.
"Look, for some reason, we were just off today. If you look at the stats of the game, we dominated and scored two tries to one, but we were a poor version of ourselves today.
"So, there is a bit of soul-searching to do, but it makes the Wales game pretty important."
Rookie Wallabies fly-half Carter Gordon had a shocker as he failed to stamp his authority on the match and was eventually taken off in the 50th minute, with try-scorer Vunivalu coming on to replace him.
Jones was asked about comments made by former All Blacks centre-turned-television pundit Sonny Bill Williams, who said that he feels sorry for Gordon that he doesn't have an experienced fly-half like Bernard Foley or Quade Cooper to talk him through his performance.
The 63-year-old responded by saying: "When you are a television commentator, you are always right. Maybe I need to become a television commentator, then I'll be right all the time. Look, we've gone with a young team; I've got no regrets at all. We are building a team for the future, and we are going to go through some pain.
"I made the decision to go for a younger team, and if that's the wrong decision, then I will be held accountable for that. But I think Australian rugby needs to move on to a younger team. I am prepared to go through some pain to leave Australia with a team capable of doing really well in a World Cup.
"That's not to say we can't do it, we've had a bit of a setback today, but that's all part of being in a World Cup. I do remember South Africa lost a game and won a World Cup, so funny things have happened."