The Swans fell to a battling 3-1 Europa League last-32 defeat at the Stadio San Paolo on Thursday, but the club claims as many as 700 of the 900 travelling supporters did not reach the stadium until 20 minutes after kick-off.
As well as delays to buses travelling from the capital Rome, Swansea also say it took more than two hours to transport 200 fans from the local police's designated meeting point in the port area of Naples, just a few miles from the ground.
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"To make matters worse, this is not the first time this has happened to visiting fans in Naples. Arsenal fans suffered the same fate there in the Champions League recently.
"We thought we had done everything possible to alleviate any issues for our fans. We sent a delegation from the club, South Wales Police and the Football Association to Naples last month to discuss previous problems with the local police.
"We thought we had made positive progress because we were given assurances that previous issues would not be repeated for Swansea City fans. Unfortunately, most of the promises and assurances we were given were not honoured on the night.
"We did everything possible on the night to rectify the situation by getting the British Consulate, UEFA delegates and Napoli officials involved. Unfortunately we had no control over events.
"As a club, we appreciate the tremendous support our fans have given us over the years. Having travelled so far to support the club at substantial cost, for them to be treated in this manner is nothing short of disgraceful.
"Our supporters were impeccably behaved in Italy and were again a credit to the club. For them to be treated in this manner is totally unacceptable."
Napoli will meet Porto in the last 16 of the Europa League.