The Northampton full-back blasted England's sloppiness after France surged into a 16-0 half-time lead with soft tries from Vincent Clerc and Maxime Medard, plus two Dimitri Yachvili penalties.
Foden's second-half try gave England a glimmer of hope, but France edged further ahead with a drop goal from Francois Trinh-Duc.
Mark Cueto wrestled his way over the line for a second England try in the closing minutes, but the dye had already been cast.
England failed to reach at least the semi-finals of a World Cup for the first time since 1999, falling short of their own minimum requirements.
The England changing room was a morbid place to be, with players still to get changed long after the final whistle.
"I am gutted and livid," Foden said. "We had a massive opportunity and we blew it. "We are just frustrated in our performance. We didn't step up to the mark.
"The French were there for the taking and we didn't step up. You don't mind losing to a better team or to a great performance, but the French weren't brilliant by any standards.
"They took their opportunities and we just didn't stack up.
"We have been waiting four or five months and to throw it away on that game is frustrating."
France had been in an apparent state of disarray since losing to Tonga last weekend and England spoke all week about preying on that mental fragility.
But England's error-strewn and ill-disciplined opening only served to embolden Les Bleus, who punished Martin Johnson's men in clinical fashion.
Clerc shrugged off Jonny Wilkinson's tackle and evaded Foden and Ben Youngs to score France's first.
Eight minutes later, Alexis Palisson drew three defenders and slipped the offload for Medard to score.
"In every game we have started slowly and we said this week if we started slowly and gave them opportunities they would punish us and that is exactly what they did," Foden added.
"How many times are we going to have to learn that lesson before we come out of the blocks with a bit of spark about us?
"The first 20 minutes we have got to look at ourselves.
"For a lot of guys that was their last quarter-final in the World Cup and to come out and concede 16 points in the first 40 minutes is just not good enough."
England's lack of accuracy cost them two promising opportunities before the interval and although Foden scored in the second half, France were never in danger.
England lost their composure, trying miracle passes and committing knock-ons in desperation to bring themselves back into the game.
"It seems like there is a lack of spark and a bit of a lack of confidence," Foden added. "The French are a good team and it was always going to be a close contest.
"It was a contest we thought we would come out on top of."
The one silver lining Johnson took from a disappointing campaign is that he believes the team can only get better in the build-up to the 2015 World Cup on home soil.
Johnson will consider his future as manager and, if he stays, the promise of players like Foden is sure to be a key reason.
"This is a big bunch of young guys and if they stay fit and fresh, hopefully we have got another World Cup in us, and when that comes around hopefully we will have a load more caps behind us and we will be the driving force in that campaign," Foden said.
"We are a talented squad but it is hard to sum up the feelings behind it.
"Johnno has been one of the inspirational guys on the tour. He took it as hard as any of the players, he might as well have been out there playing it with us.
"You could see it in his face, he was just as gutted as the players. He came round and consoled - he understands - it is part of being a professional rugby and sometimes it is a hard pill to swallow.
"Today was one of those occasions."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.