Rafa Benitez's men had to settle for third last term as the Bianconeri romped to a third-straight Scudetto crown, despite significant pressure from Rudi Garcia's side in the first half of the season.
However, Hamsik feels that his team should be aiming for success in all competitions this time around as they look to defend their Coppa Italia crown and progress further in the Champions League.
"Napoli should always be aiming high. We want to win the Scudetto, the Coppa Italia and go far in the Champions League," the midfielder told reporters.
"The team is ready to give its all. We are no worse than Jvuentus and Roma. They did some extraordinary things last season, while we lacked some consistency, but we're not inferior to them.
"I really want to win the Serie A title. It would be amazing for the city and for us. We need a perfect season to achieve it, though. We are strong and can aim high.
"Juventus are always the favourites and then there's Roma, Inter and AC Milan. It will be a competitive competition again."
Napoli last won the Scudetto in 1989-90, when Diego Maradona and Careca guided them to their second ever league title with 16 and 10 goals, respectively.