The win kept Carpi, who are 17th and hovering just above the drop zone, one place and three points clear of Palermo, who won a key relegation battle away to Frosinone (19th) on Sunday to revive their own chances of staying up.
The bottom three in the 20-team table are relegated.
Palermo's official website (www.palermocalcio.it) listed what it called "three absurd episodes" during Carpi's win and provided screenshots of incidents where the Sicilian club claimed that the referee had made the wrong call.
It also included a comment from Empoli coach Marco Giampaolo, who told Skysports Italia: "The other teams fighting against relegation must by very angry about this match."
Palermo then invited the league's disciplinary tribunal to "monitor with great attention the next matches and all the teams involved in the battle to stay up, to avoid similar episodes".
Palermo's volatile president, Maurizio Zamparini, said he feared that "they want to send Palermo into Serie B".
"I don't know why, but I fear that's what is going on," he added, without elaborating.
The Italian league generally avoids comment on conspiracy theories and has not replied, but Carpi president Stefano Bonacini hit back.
"I have the good grace to never speak about referees in a negative or positive way," he said. "We are not interested in whatever statements others release. We are fighting for our safety tooth and nail."
Palermo have an excellent chance to draw level with Carpi on Sunday as they host Sampdoria (1300 GMT) while their rivals are away to newly crowned champions Juventus (1030 GMT), who have won 24 of their last 25 league games.
There are two matches remaining after this weekend and should Carpi and Palermo finish level on points, relegation will be decided on goal difference as they are level on their head-to-head record.
Frosinone, a further two points below Palermo, visit AC Milan while bottom club Verona area already down.
Most commentators feel that Zamparini would have only himself to blame for Palermo's demise after overseeing an astonishing eight coaching changes this season.
Davide Ballardini, the latest incumbent, is one of two coaches who have had two stints at the Sicilian club since August, having been sacked in January and re-hired two weeks ago.
(Editing by John O'Brien)
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