Emanuele Calaio haunted his parent club, coming off the bench to score a stunning 84th-minute free-kick to earn Genoa a surprise point at the Stadio San Paolo – a goal he apologised for.
Gonzalo Higuain put Napoli ahead on 18 minutes in front of their home fans with a chipped finish, but the third-placed Serie A side were unable to seal the result.
Benitez said he wanted several more goals during the first half and felt Genoa were always likely to respond after his team failed to score again before the break.
"The first half was the key for me, as we wanted to score two or three goals and then control it after the break," the Spaniard told Sky Sport Italia.
"We didn't achieve that, we knew they were dangerous and that at 1-0 we were always in the balance.
"Clearly if we win our games, then it's easier to think we can finish second. We must understand that this type of match has to be finished off by half-time and that is all."
Higuain's clever finish from a Marek Hamsik pass appeared to have Napoli on track for the first-half target Benitez had set them.
But Calaio, who came on in the 63rd minute, hit back with a delightful, curling left-footed free-kick from 35 yards to earn Genoa a point.
Calaio helped Napoli from Serie C1 to the top flight with several goals during seasons 2005/06 and 2006/07 and the 32-year-old rejoined them in January 2013, only to be loaned out.
He waved apologetically to the crowd as his team-mates celebrated with him after his goal.
"I'm sorry to have scored at Naples," Calaio said.
"Sorry to do this here at the San Paolo but this is my job.
"When the coach gives me the opportunity I always try to give the maximum satisfaction and perform for this shirt. They deserve it, these fans who have come this far."
Genoa coach Gian Piero Gasperini said: "Calaio cared so much about being here in this stadium, so it wasn't easy for him.”
Gasperini praised his younger players, including striker Moussa Konate, with Genoa sitting 11th in the Serie A.
"(Moussa) Konate only just turned 20 and has already made a lot of progress from a few months ago," he said.
"He's growing from game to game and we have an excellent group of young players who are being helped by the experienced figures.
"We don't tend to have great ballistics specialists, so we tend to have to build our moves and get close to the goal in order to score.
"It might seem as if we don't create many chances, but in reality we just take longer to get there."
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