Fans clashed with police in the Italian city prior to the match which Napoli won 3-0 to advance to the last eight.
Italian police arrested both Napoli and Eintracht supporters.
"We remain convinced that blanket ticket sales bans, or even entry and travel bans, will not achieve anything," Eintracht board member Philipp Reschke said in a club statement.
"You deprive thousands of supporters of the opportunity to see such a game, poison the already tense atmosphere, and in the end you still can't prevent those who go looking for like-minded people from doing so."
"Everything was prepared and organised, from the fan meeting point to the transport and so on. This organisation was replaced by improvisation and chaos. That doesn't justify anything, but it's part of the story," he said.
Italian authorities had banned German fans from attending the match amid concerns about possible violence following clashes after the first leg.
Eintracht's attempts to overturn the ban failed but a group of the German club's supporters made the trip to Italy anyway.
Fans then clashed with anti-riot forces before the game and set fire to a police car, with objects being tossed towards the police while overturned tables and chairs lay smashed on the ground.
"We regret extremely what happened here," Reschke said. "There is absolutely no justification for this violence. We may all have feared it, but it is and remains unacceptable."
"It harms football, it harms Eintracht Frankfurt and it harms our efforts to stand up for the rights of all fans who would've liked to see a football match in the stadium here without repression and decree."
