Ronaldo bagged a brace in the second half to inspire the reigning European champions to a 3-0 win over Hungary in their opening game at EURO 2020.
The Juventus star used his trademark 'siu' celebration after making it 2-0 from the penalty spot, although Rossi was not too pleased.
"Ronaldo is a great champion but at times he can be annoying," Rossi told La Gazzetta dello Sport.
"After the penalty with us he celebrated as if he had scored in the final. People notice these things."
Despite going out in the group stages, Rossi was happy with how his Hungary side performed in the 'Group of Death'.
"I don't give a damn about revenge and I'm not interested in returning to Italy," he said. "I'm happy if I left a footprint in Hungarian football.
"I slept a maximum of 15 minutes last night and it's weird.
"I would never have thought that a draw with Germany would leave me with this feeling. I know we were good but I'm sorry."