Liverpool manager Jurgen Klopp was left frustrated by what he saw as a "clear and obvious" mistake on a penalty call against the Reds, although the German coach also admitted his side were not at the level needed to win against Napoli.
On Tuesday, the defining moment came from the spot as Andrew Robertson was penalised for a foul in the box on Jose Callejon in the game's waning moments.
Dries Mertens buried the ensuing spot-kick, although many viewed the penalty call as soft.
Napoli were then able to seal the victory late on through Fernando Llorente, who intercepted a backpass from Virgil van Dijk to double Napoli's advantage and lock up three points.
After the loss, Klopp was upset with the referee's decision, although he also expected more from his players on the day.
"What can I say? For me, it's clear and obvious not a penalty because Callejon jumps before there's any contact. But we can't change that. We have to be critical with ourselves. We could have done better," Klopp told BT Sport.
"They did well in a lot of moments, we played a lot of good football that we didn't finish off. We had our chances. There were moments when we wanted a free kick. I don't understand why there was no free kick when Sadio [Mane] goes down, up and down, up and down. You think 'what's happening here?'
"It kept the intensity of the game, but what I said, we controlled moments but didn't have a lot of chances at the end. You saw a lot of respect from both sides where we both defended well, but each ball we lost or they lost was immediately a threat.
"In these situations, you have to finish it off. I think one situation, Sadio was running, if he makes two more steps and shot, but from the beginning he wanted to pass the ball, in the end you're like make another step and you can do it yourself.
"We made these decisions that were not right tonight and we have to accept the result."
In particular, Klopp was left disappointed by his side's lack of sharpness on the ball, as Liverpool wasted several counterattacks while proving ineffective in possession.
As a result, Liverpool were left with their first loss of the season, having won the first five Premier League matches of the new campaign.
He added: "It should hurt because there were opportunities to win the game. This was a much better game than the last time we played them and they won 1-0 in the last minute. It was an open game.
"There were moments when we controlled the game, we had a lot of counterattacks but didn't finish them off. That's a problem.
"In the second half, we had this wild game. We were running, they were running and that killed everyone on the pitch.
"Then we started controlling it again but conceded a penalty. That doesn't help. I don't think it's a penalty. I've really no idea. It's difficult."