The midfielder took a penalty with just over 10 minutes to go that would have been an equalizer, but she hit the ball wide of the right post and Japan won 2-1 on Monday.
The world champion held off France, often desperately, for the remainder of the match and will now play in Thursday's final against the United States at Wembley Stadium. It will be a rematch of last year's World Cup final, won by Japan on penalty kicks.
"I feel horrible," Bussaglia said. "It is a shameful feeling. I opened up my body too much and the ball went wide. We miss the final now, so it is a big disappointment. We are all very sad. But we have a bronze to play for so we must recover for it."
The loss was especially hard for France because it was knocked out of the World Cup after reaching the semifinals.
Japan, which had only conceded once in the tournament before Monday, went into the match as the favourite, but France had the better of the opening exchanges with Elodie Thomis and Marie-Laure Delie both looking dangerous down the flanks.
Yuki Ogimi gave Japan the lead in the 32nd minute after an error by France goalkeeper Sarah Bouhaddi, who went to meet a free kick but fumbled an easy catch. The team's top scorer at the London Olympics got to the rebound first and bundled the ball in from close range.
Three minutes into the second half, Japan doubled its lead when midfielder Mizuho Sakaguchi looped a header into the top right corner.
France coach Bruno Bini brought on striker Eugenie le Sommer soon after, and the substitute galvanized the team.
She scored in the 75th, firing in a cross first time, and won the penalty a minute later after she was bundled over running onto goal.
France attacked in waves for the last 10 minutes of the match, with le Sommer coming close again with an overhead kick that was saved. Ogimi then the hit the post in the 90th after breaking from the halfway line.
"They were an amazing team, but we had the most passion," Japan captain Aya Miyama said.
Wendie Renard and Louisa Necib each came close for France in the four minutes of extra time, but again were denied by keeper Miho Fukumoto.
"Today was even more disappointing than the world cup," said Bini. "In the last 20 minutes we played very well and were even better than Japan. They barely reached our side of the pitch."
Japan coach Norio Sasaki said he would be taking his team out for a Japanese meal to celebrate winning a medal, but that he was focussed on Thursday's final. He praised a motivational speech made by Miyama before the match in which she said she "was happy to be here on this wonderful pitch with these wonderful teammates.
"It made me cry," he said. "The difference today was in our mentality."