Rafa Benitez's men sit three points behind Roma, having played a game more, after Jose Callejon scored the winner nine minutes from time at the Stadio San Paolo.
Despite seeing Napoli take revenge for their two defeats against Roma earlier this season, Garcia was buoyed by the performance but lamented the lack of cutting edge on show.
"We lost effectiveness in front of goal and also a bit of luck," he told Sky Sport Italia. "We definitely need to get back that killer instinct.
"It was possible to create scoring chances with so much speed. They came but unfortunately we couldn't put them away.
"You also need a bit of luck to score. Our shots grazed the woodwork while theirs hit the bar and went in.
"We played with maturity and personality. We didn't deserve the result but that's football. The best team doesn't always win."
Garcia also expressed concern over the injury suffered by Kevin Strootman, with the midfielder forced off after just 13 minutes.
"The main concern is not the defeat but Kevin Strootman and we hope that we haven't lost him for a while," Garcia added.
"He is in a lot of pain, the knee is swollen and he had a nasty knock, then sprained it a few minutes later."
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