Rafael Benitez's men kicked off their campaign with a commanding 3-0 victory over Bologna on Sunday night, with their Slovakian star netting twice after Jose Callejon had opened the scoring at the San Paolo.
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"They are favourites, but we will focus only on our games," the attacking midfielder is quoted as saying by Gazzetta dello Sport.
"But certainly I hope that to have started the season in this way shows we can win something. We'll put it all on the line; we will give our best.
"We were convincing [against Bologna]. But we also know that there is much to improve. The important thing was to start with the right foot and we managed that. We're definitely on the right track."
Hamsik has been repeatedly linked with some of the top clubs in Europe but he says that he could not be happier in Naples.
"I've never felt the need to change city," the 26-year-old insisted. "I don't want that. I feel loved by fans; I do not need anything else."
Hamsik joined Napoli from Brescia six years ago and has since established himself as one of the most effective attackers in Serie A.