Conte is accused of failing to report alleged match-fixing involving Siena when he managed them in the 2010-11 Serie B season.
The club's plea bargain deal was accepted, meaning they will start the new Serie A season with a six-point deduction, but Conte's proposal - which would have seen him serve a three-month suspension and pay a fine of 200,000 euros - was turned down.
He will now have to either submit a new offer or face a sports tribunal, with either option likely to lead to a longer ban.
Charges against Conte of direct involvement in match-fixing were dismissed last week but, having originally denied all charges, he later tried to reach a compromise deal over failure to report the alleged misdemeanours going on within his team.
Siena saw an initial proposal of a five-point penalty rejected, but a second offer of six points was approved.
President Massimo Mezzaroma told the club website: "The plea bargain allows us to finally turn the page, as we all want.
"This penalty should be a further incentive for everybody.
"We will demonstrate on the field that we can earn our salvation, even starting with this initial handicap, thanks to our values and our ability to overcome difficulties."
The club also saw striker Marcelo Larrondo banned 16 weeks and fined 30,000 euros, while goalkeeping coach Marco Savaroni and fitness coach Giorgio D'Urbano will serve 23-week bans.
Serie A newcomers Torino, Serie B side Varese and relegated Albinoleffe will pay fines of 30,000 euros and begin the season with one-point penalties after their plea bargains were also accepted.
Lower down the league pyramid, Grosseto were relegated from Serie B and docked three points, Novara were penalised four points and Ancona were fined 10,000 euros.
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