Conte, who led an undefeated Juventus to the Italian title in his first season in charge last term, was banned on August 10 for failing to report two incidents of match-fixing in the 2010/11 season when he was coach of then Serie B side Siena.
The Italian federation (FIGC) said in a statement on Wednesday that Conte, whose hearing was heard on Monday, had lost his appeal over the sentence.
Juventus President Andrea Agnelli said the ruling confirmed the club's "worst suspicions" about Italy's football justice system which "seems more and more like a witch-hunt".
The FIGC's prosecutor also lost an appeal against the decision to acquit Juventus defender Leonardo Bonucci and winger Simone Pepe over an alleged attempt to fix a match between Bari and Udinese in 2010.
The FIGC's prosecutor had wanted a three-and-a-half year ban for Italy's Bonucci, who was playing for Bari at the time, and one-year ban for Pepe, who was with Udinese.
The Serie A season starts this weekend. Juve have said they will stick by Conte with a second appeal set to be launched and heard in September.
Conte's assistant Massimo Carrera has taken charge of Juve's pre-season friendlies and is poised to stay as temporary boss.
The Siena matches that came under scrutiny were against Novara and Albinoleffe in May 2011. FIGC's appeals tribunal said Conte had now been acquitted over the Novara game but that the 10-month ban should stay for the Albinoleffe affair.
Agnelli highlighted the fact that Conte had been cleared for one of the two games he had originally been punished for and his main accuser had been discredited, yet the sentence had not been changed.
"Enough is enough," he said in a statement posted on the club's website. He slammed the "profound injustice" of the sentence and confirmed that Juventus would appeal again.
Siena had already been fined while Conte's assistant at Siena and Juventus, Angelo Alessio, was banned for eight months. His suspension has been reduced to six months on appeal.
Grosseto, also dragged into the probe into illegal betting and match-fixing across the Italian game, had their demotion from Serie B reversed by the appeals panel and their president cleared with second tier Novara having their points penalty cut to one from two.
All other sanctions including Lecce's demotion to the third tier remain.
Italy has suffered an array of match-fixing scandals over the years. Juve, the country's best supported and most successful club domestically, were demoted to Serie B in 2006 and struggled to regain their former glory before last term's triumph.
They now face difficulties again despite the club not being directly involved.
The suspension is for all club activity so Conte will also not be able to coach Juve in their return to the Champions League.
The mechanics of the ban are far from clear and he will be able to influence the team from afar.
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