Speaking at a charity event, the Slovakian looked ahead to pre-season preparations and the Partenopei's chances of glory in 2012-13.
"On Sunday we return to Naples, and on Tuesday we leave for the training camp," Hamsik told Pravda.
"We expect hard training and then another difficult season where we want to achieve great success."
As well as a fifth-placed finish in Serie A, Walter Mazzarri's men toppled undefeated league champions Juventus in the Coppa Italia final, with Hamsik sealing victory late on.
They also reached the last 16 of the Champions League after negotiating a group containing Manchester City, Bayern Munich and Villarreal.
"I have great expectations for next year," Hamsik added. "The club will do well in the transfer market and replace Lavezzi in the best possible way."
The Argentine forward joined Paris Saint-Germain on Monday after a five-year spell in Napoli, in which he scored 48 goals in 188 games.