Rafael Benitez's side were knocked out of the UEFA Champions League in the play-off round by Athletic Bilbao and went on to lose two of their opening three league matches.
Three successive victories in all competitions before the international break helped ease early concerns at Stadio San Paolo.
Hamsik is aware Napoli need to keep up the winning habit if they are to close an eight-point gap to leaders Juventus, but expects his side to shine when they return to action after the international break.
"I believe we are still in the race for the Scudetto, but we can't afford to drop too many points on Juventus and Roma," the attacking midfielder told Top Mercato.
"We've started badly, but we're a big team with a lot of talented players, so I think we're still in the running.
“There are still a lot of games to go until the end of the season, so we have the chance to recover.
"We have already lost two games in the league, which is too many after only six games.
"I believe that from now on we will do much better, I'm convinced the break will be good for everyone.
"It will allow us to reach top fitness and raise the level of our game."
Napoli travel to the San Siro on Sunday hoping to inflict a third successive defeat on Walter Mazzarri's Inter.