"If you don't believe in the good faith of the referees...it's better to stop," Allegri told Italian media.
Juve were held 1-1 at home by lowly Genoa on Saturday and believed they should have been given a penalty in stoppage time when Andreas Granqvist kicked the ball on to his hand.
Coach Antonio Conte, whose side are three points clear of second-placed Napoli, was livid and said referee Marco Guida told him he "was not ready" to award the penalty.
"I accept being told 'we made a mistake and we're sorry' but I can't accept being told 'I don't feel like I could give it'," explained Conte.
"If the assistant and the fourth official both say it was a penalty then the referee can't say 'I wasn't able to give it'. That isn't football," he said before adding the incident was "shameful".
The most controversial remark came from Juventus sporting director Giuseppe Marotta who made a reference to the fact Guida comes from the Naples region.
"In the 94th minute a referee from the Naples region found himself in a difficult situation," said Marotta.
That comment was badly received especially as it was far from clear whether Granqvist's handball was intentional.
Genoa president Enrico Preziosi described Conte's reaction as "arrogance" and demanded action.
Di Sanctis also said Juve's comments should be investigated.
"All the gossip by the Juventus team, in my opinion, should be analysed in great detail and I hope those responsible will do so," said Di Sanctis.
Napoli coach Walter Mazzarri, whose team won 2-1 at Parma on Sunday, preferred to stay out of the row.
"I am not interested in talking about this," he said. "Once it (the season) is over I will express my opinion."

However, Nocerino says there is little prospect of a January transfer.
“I’m happy at Milan,” he said. “Then, if the club decide to put me on the market, we’ll sit down and discuss it together.
“I don’t think that I’ll be leaving in January. At the end of the season we’ll evaluate what I’ve done well and badly.”
Nocerino joined Milan at the start of the 2011-12 season from Palermo and has scored 13 goals in 68 appearances for the Rossoneri.

A statement on Wigan's official website read: "Wigan Athletic can confirm that Mauro Boselli has joined Italian Serie A side Palermo on loan until the end of the season with an option to buy at the end of the term."
Boselli has made 12 appearances for Latics so far this season and scored four goals in all competitions.
It will be his second spell in Italy after a loan stint at Genoa last season which returned just one league goal from six appearances.
Boselli joined Wigan in 2010 from Estudiantes, to whom he returned for a loan spell at the beginning of the 2011-12 campaign.
In all competitions he has made 24 appearances and scored five goals for Roberto Martinez's men.
Palermo confirmed Boselli's arrival at the Stadio Renzo Barbera with a brief statement on their official website, with the striker set to be unveiled at a press conference scheduled for 1pm BST on Tuesday.

City have not been actively trying to sell Balotelli, who has never been far from the headlines with a series of on- and off-field antics, but if he were to leave the club in this month's transfer window it would not be on a loan deal.
Balotelli joined City from Inter Milan in 2010 for around £24m and has had a sometimes troubled time at the club, including clashes with manager and compatriot Roberto Mancini and disciplinary issues.