Wales' memorable run at the tournament - their best in a World Cup since 1987 - ended after France ground out a 9-8 win.
Wales had captain Sam Warburton sent off for a dangerous tackle on France wing Vincent Clerc inside the opening quarter, which came just eight minutes after prop Adam Jones went off injured.
But despite being a man down, Wales threw everything at their opponents and scored the game's only try through scrum-half Mike Phillips, but four missed kicks at goal cost them.
"We came to the World Cup honestly believing that we could win it," Charteris said.
"It's not to be now, and the boys are devastated. It's heartbreaking for Sam and for the whole team.
"No one is blaming Sam at all. He has been outstanding all tournament. It's not like it was a reckless or a stupid thing.
"He put a good tackle in. How it was a sending off I've got no idea.
"The boys showed great heart and effort to not let a team of France's attacking powers score a try when down to 14 men."
Wales went through 27 phases of play in the dying minutes, but they were unable to manufacture a potential match-winning position, either with ball in hand or via the boot.
Fly-half Stephen Jones, who replaced an out-of-sorts James Hook early in the second period, said: "I was thinking of the drop-goal. I just wanted us to get a little bit closer.
"France were smart. They decided they weren't going to flood the contact area, they were going to flood the front-line. One guy takes the tackle and everybody else wouldn't contest the ball.
"They just waited for us to relaunch another attack, and of course, it was very hard for us to get going. They knew what we were trying to do, and they nullified our threat."
Centre Jonathan Davies admitted it was a golden opportunity that went begging for Wales, who will now play New Zealand or Australia in the third place play-off match next Friday.
"We caused France more trouble than they caused us," he said. "It's just frustrating we didn't get the result we deserved.
"We were the better side, but in the end we didn't get the result. Maybe it was a lack of patience, because towards the end we got a bit ragged and lost structure.
"Sam spoke to us after the game and told us to hold our heads up. He had asked us to be brave at the start of the game and I think we were.
"Before the tournament, nobody gave us a shot of coming third in the World Cup, so we will definitely be up for it on Friday."
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