The 24-year-old has complete faith in the club's project and urges the team to focus on their upcoming matches, rather than worry on the results of their rivals
The Slovakia international added one year to his previous deal to put an end to speculation about a potential move away from the San Paolo.
"I have renewed my contract because I believe in Napoli and because I feel fine here," Hamsik told Sky Sport Italia.
"If I prefer to win the Coppa Italia to finishing third in Serie A? I do not rule anything out, we are playing for both things.
"It is a shame that we crashed out of the Champions League, but we did well and we want to continue like this."
Napoli face the threat of Lazio, Udinese, Inter and Roma for a top-three finish, but Hamsik insists that he does not fear any particular club.
"I am only looking at Napoli, not the other clubs," he added. "If we do well, then we will see what happens.
"If we get good results and win all of our matches, we can finish third. We must look at ourselves only."
The Partenopei will visit Roma on Saturday in their next Serie A game.