The game at the Stadio Olimpico was delayed by 45 minutes after trouble between the two sets of supporters was compounded by news of three men being shot by police in Rome, an incident authorities later insisted had nothing to do with the match.
Hamsik was forced to speak to leaders of Napoli's ultras before kick-off to calm the situation and he conceded after the 3-1 win that the pre-match troubles were hard to shake off.
"It was a very difficult night. Every final is complicated, but at the end the emotion of the victory put everything behind us," Hamsik told Rai Sport.
"We are professionals and know these things can happen. We had to concentrate on the field and that’s all that matters."
The Slovakian international said the triumph was a fitting end to a season which saw coach Rafael Benitez take charge and a host of big signings, such as Gonzalo Higuain and Jose Callejon, brought in.
"This season we changed coach and system, so it was important to lift this trophy and pay off our hard work," Hamsik said.
"I dedicate the Coppa to all our fans, my wife and children."
