The Senegal international initially started well making a double block from Aaron Ramsey.
But Arsenal quickly found themselves 2-0 ahead with Koulibaly involved in mistakes for both.
He was nutmegged in the build-up to the first swept home by Ramsey.
And then Koulibaly was credited with an own goal for the second as he diverted a Lucas Torreira shot past a helpless Alex Meret.
And fans were quick on social media to rubbish suggestions that the centre-back is better than Liverpool ace Virgil van Dijk.
One tweeted: “This the Koulibaly that’s supposed to be better than Van Dijk?”
Another added: “Koulibaly used to be better than van Dijk according to rival fans. Absolute jokers.”
A third explained: “People saying Koulibaly > Van Dijk.”
“Nutmegged on the pass before the first goal; deflects in the second goal. Koulibaly is the best defender in the world, eh?” another said.
Koulibaly is on the radar of Chelsea and Manchester United as he is expected to leave Napoli this summer.
But his first half display may leave some fans hesitant about the qualities of the 27-year-old.
Koulibaly has impressed this season, making 41 appearances in all competitions.
But he had a torrid time in the first half at the Emirates.
Arsenal will look to increase their lead in the second 45 minutes to out the tie beyond Napoli.
The second leg takes place next Thursday.
And with the Gunners fighting to finish in the top four they may see winning the Europa League as a better opportunity to qualify for the Champions League next season.
