Limbach was ousted 15-12 in a tense quarter-final by Nikolay Kovalev of Russia, leaving the semifinals without any of the top four seeds.
"The disappointment is huge, I wanted to win obviously," Limbach said. "But I knew the medals were not just there to be picked up."
Earlier, world and former Olympic champion Aldo Montano lost 15-13 to Italian teammate Diego Occhiuzzi, Russia's main medal hope Alexey Yakimenko was upset 15-14 by Daryl Homer of the United States, and fourth-seeded Bongil Gu of South Korea lost by the same score to Germany's Max Hartung.
Defending Olympic champion Man Zhong of China went out in the last 16. After edging Kim Junghwan of South Korea 15-14 in his opening match, Zhong was beaten 15-10 by Aron Szilagyi of Hungary.
Kovalev will play Szilagyi in the first semifinal, followed by Ochhiuzzi taking on Rares Dumitrescu of Romania, who defeated Homer 15-13.
"These are the Olympics, this can happen," Limbach said. "It shows you how tight the top in sabre really is."
Limbach struggled to find his way into the match against the very attacking Kovalev, who went 4-0 and later 7-3 up. Limbach seemed to have found his stride as he scored five straights points. Later he rallied from 9-12 down to level at 12-12.
"I never felt I had the momentum with me," Limbach said. "I had to fight hard for each of these points. He left me few opportunities to play my own game and he had some really good attacks."
World champion Montano missed over one month of training building up to the Olympics because of a left-thigh injury. He battled back from 11-5 down to trail by just one point at 14-13 before Occhiuzzi closed out the victory.
"I was afraid to tear the muscle so I tried to stay on the defensive side," Montano said. "Occhiuzzi knew of my problems and rightly took advantage."