Cavani scored the second in Napoli's 2-0 win over Chievo to give Walter Mazzarri's side their first league win since January 8.
The Uruguayan's spot kick doubled Napoli's advantage after Miguel Britos had earlier put Napoli in front at Stadio San Paolo.
"We had a good match in terms of intensity, character and desire," Cavani told Mediaset Premium.
"This was a difficult moment, but I think we responded the way we wanted."
Cavani was understandably in confident mood after Monday's win and he warned Chelsea not to take the Serie A outfit lightly when the two teams meet in the knockout stages of the UEFA Champions League next week.
Napoli has already knocked out one English club in the competition this campaign - they finished second and above current Barclays Premier League leaders Manchester City in the group stage to consign Roberto Mancini's expensively assembled squad to an early exit from Europe.
"We have already sent out a message to the world: we can defeat anyone," Cavani said.
"Chelsea must be careful with us."
Napoli and Chelsea meet on Tuesday February 21 at Stadio San Paolo for the first leg.