The match finished 0-0 following extra time, with Australia goalkeeper Mackenzie Arnold saving three French penalties before Cortnee Vine scored the winning spot kick to make it 7-6.
France, who were looking to reach the semi-finals for the second time after 2011, had their fair share of chances, and Renard said the match could have gone either way.
"It's very difficult to fight against these things but unfortunately we weren't able to quite clinch that win," Renard told reporters. "I've got nothing to criticise. Everyone worked exceptionally hard. We have no regrets."
Renard opted to bring on goalkeeper Solene Durand to face the penalties in place of starting stopper Pauline Peyraud-Magnin, with the substitute making some key saves in the shootout.
The Frenchman said the substitution had been planned well in advance, adding: "All of us knew the qualities of Durand, she's amazing on the penalty shootout.
"If we won this evening, I would be king of the world, but this evening I'm nothing because we lost by some millimetres. This is football but it's also why we love football, because I think all the people watching this game were enjoying (it).
"I think it was a fantastic image of women's football."
Renard said he and his squad would quickly turn their thoughts to next year's Olympic Games on home soil in Paris.
"We're going to continue to progress and we're going to keep this mindset and everything will be fine," Renard said.
"We're just going to continue this year 2023, get off to a good start for 2024 with the Nations League and then we'll be preparing for the Olympic Games.
"We're hoping that we'll be able to recover some of the players that maybe we were missing from the squad this time around. That's once again part and parcel of football. This will allow us to become even stronger."
