State broadcaster Rai also became embroiled after Napoli suggested their supporters should watch the match with the sound turned down.
Napoli were left fuming after an incident in the 69th minute when they had a penalty appeal turned down and Juventus, who were leading 2-1 and had already been awarded one penalty, broke upfield and were given another, which they converted.
Naples Mayor Luigi De Magistris issued a statement on the city government's website to express his anger over both the refereeing and what he alleged were anti-Naples chanting by home fans and unfair commentary by Rai.
"Yesterday, in Turin, we suffered a continuous injustice, a game littered with and influenced by repeated refereeing mistakes and shameful chanting about the city," he said. "It was a disgrace on top of disgrace."
He also criticised Rai's commentators, saying they "saw a different game and told a story that did not happen."
The club also criticised Rai during the match, using the hashtag #ifyouarewatchingthegameonRaidoitwithouttheaudio.
Rai commentator Marco Mazzocchi said the tweet was unacceptable. "It's something a fan could tweet, but not a club," he said.
The Juventus-Napoli rivalry, in particular, has been punctuated by rows. Napoli were so upset at their 4-2 defeat by Juventus in the 2012 Supercup match, played in Beijing, that they boycotted the medals ceremony at the end.
The row came hot on the heels of two controversial matches on Sunday.
AC Milan beat Sassuolo on a penalty converted by Carlos Bacca, who slipped as he went to kick the ball and appeared to touch it twice.
AS Roma's 3-1 win at Inter Milan also featured controversy over some refereeing decisions, although the complaints came from the media rather than Inter themselves.
"I'll say just one thing, it's all pub talk," said Juventus defender Giorgio Chiellini after Tuesday's game.
"I watched the Inter-Roma game on Sunday and I saw a team (Roma) that deserved to win, that clearly dominated their opponents. But when I read the match reports, they spoke about everything but Roma's performance."
"The same thing happened tonight," he said, adding that Napoli should focus their efforts elsewhere. "In the end, they are just wasting energy on this and it doesn't affect us."
(Writing by Brian Homewood in Berne, editing by Larry King)
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