The forward was taken off with suspected knee damage after the Livorno defender's foul, leaving both the Viola president and Vincenzo Montella angered
Rossi had to be withdrawn midway through the second half after a robust challenge from the 30-year-old, with the Italy forward set for scans on Monday to determine whether he may have damaged the same knee ligaments which have twice been operated on in his career.
Rinaudo insisted after the match he made no effort to injure Rossi and was prevented from apologising to him after the final whistle, but Della Valle was nonetheless incensed at the player's actions.
"We are very concerned. Rinaudo hasn't even gone to apologise," he told reporters after the match.
"This is not football. Rossi is down and I would like to say many things. We need to reflect, but I can tell you one thing: Rinaudo is a scoundrel."
Fiorentina boss Vincenzo Montella said he could add little before Monday's tests had been conducted, but made it clear he was not impressed with the tackle.
"We're all concerned. Tomorrow we'll know, there's not much to say now," he said. "It looks like a deliberate foul, not in the sense that he wanted to hurt him, but that he wanted to get the player.
"I would expect an apology from Rinaudo. Even though he was also complaining, he had no chance of winning the ball.
"The performance today was not the best because Livorno closed any space. What counts for us is to get the three points."
Gonzalo Rodriguez's second-half goal was enough to secure maximum points for the Viola as they returned to action following the winter break.