The defender insists he was not out to injure the attacker after his challenge left the Fiorentina star facing a potentially serious knee injury.
Rossi had to be replaced in the second half after Rinaudo caught the Italy international's knee with a robust challenge - the same knee which has twice required surgery to repair damaged ligaments.
Fiorentina president Andrea Della Valle labelled Rinaudo a "scoundrel" after the match while Vincenzo Montella slammed the 30-year-old for not apologizing for his actions, but Rinaudo has stressed he was stopped from doing so outside the dressing rooms.
"It was a normal foul in the game. On the pitch, I didn't apologize because I was protesting with the referee," he told Sky Sport 24.
"I wanted to go to talk to Rossi in the dressing room but there was a wall of people who blocked me and I couldn't. I'll do so in the coming days.
"I hope his injury isn't serious."
Fiorentina secured a 1-0 win in Sunday's meeting courtesy of Gonzalo Rodriguez's second-half strike.