Gonzalo Higuain put Napoli ahead after 24 minutes before Valon Behrami netted an own goal to level two minutes later.
Goran Pandev restored Napoli's advantage five minutes into the second half and Higuain doubled his personal tally in the 72nd minute. And, after Keita Balde Diao momentarily reduced the deficit, Jose Maria Callejon made it 4-2 in stoppage time.
The result leaves Lazio with just one victory from their last nine Serie A fixtures, piling the pressure on coach Petkovic, who feels his side deserved more.
"We are lacking results at the moment, but we deserved more," he told Sky Sport Italia.
"We made four mistakes at the back and Napoli took advantage of all of them with their ruthlessness. I tip my hat to them, because they didn't let us get away with anything."
Home fans at the Stadio Olimpico staged a protest after the match, but Petkovic is unconcerned.
"The fan protest? I don't think anything has broken between the team and the fans," he continued. "We deserved more and have to be more efficient in proving that on the pitch.
"We played on a par with Napoli, but that was not enough.
"The confrontation with the fans is necessary, whether positive or negative, because we must all be moving in the same direction."
The 50-year-old has been linked with a move to replace Ottmar Hitzfeld as Switzerland coach, but refused to discuss the situation following Monday's defeat.
"I don't want to keep repeating the same answers and this is not the right place to respond," he added. "These rumours are part of the game and you have to accept them."
