The Azzurri were expected to challenge for the Scudetto last season but eventually finished fifth in the Italian first division.
In 2010-11 Napoli finished third and qualified for last season's Champions League, but the departure of star forward Ezequiel Lavezzi means that they may find it difficult to repeat that feat.
However, Hamsik believes that coach Walter Mazzarri has a strong squad at his disposal but refuses to hype up talks of winning the league title.
"We have proved in the last two-and-a-half years that we can challenge anyone," the Slovakian told Radio Marte.
"We've got to be concentrated for the whole campaign and do much better against the small clubs.
"I don't want to talk about the Scudetto. We've been together for many years, the squad is fired up and those who just arrived can lend a hand. We can go far this season."
Hamsik also cooled down speculation on his future at Napoli and affirmed his commitment to the former Italian champions.
"This is my home and I am not thinking about anything else," said the 25-year-old. "I want to do well with this jersey and the fans deserve it too."
Napoli will begin their 2012-13 Serie A campaign with an away game against Palermo on Sunday, August 26.