Hamsik declared the club's fortunes are in their own hands, hinting that Napoli at their best should be able to push reigning champions Juventus and other potential rivals all the way in 2014-15.
Napoli were heavily involved in the race for the Scudetto for the first half of last season but a 3-0 loss at Juventus in November, followed by a 1-0 home defeat to Parma saw Rafael Benitez's side fall six points behind the eventual champions and they never recovered.
Juventus eventually won their third straight Italian league title with a record tally of 102 points, 17 ahead of Roma, while Napoli claimed third with 78.
But Hamsik believes Napoli should be much closer to the Serie A championship in the new campaign.
"Napoli fans dream of winning the Scudetto, it is a goal we want to achieve," the Slovak told Sky Sport Italia.
"We are aware of our strength and we want to do well. It's all in our hands."
Napoli could also be playing in the UEFA Champions League this season, with Benitez's men having been handed a spot in the play-off round after finishing third in 2013-14.
Callejon does not want Napoli to preference Serie A over the Champions League or vice-versa.
The Spanish winger wants Napoli to aim high in both.
"As far as I'm concerned we should never limit ourselves," Callejon told E' Azzurro.
"Scudetto and [the] Champions [League], do not let us place limits on ourselves.
"Of course, let's focus on one challenge at a time. We [need to] win the preliminary [tie] to enter the main draw. Of course not underestimate the Scudetto either. The Scudetto is an important goal."