The 51-year-old coach is not giving up Napoli's pursuit of the Scudetto this season, despite their chances being dealt a huge blow by falling nine points behind Juventus
The Partenopei went down 2-0 away to Chievo on Sunday, while rivals Juventus dug deep to record a 1-0 victory over Catania.
However, despite the Bianconeri now holding a seemingly unassailable lead over Mazzarri's team, the 51-year-old hopes his side can still catch Antonio Conte's men.
Speaking to Sky Sport Italia, he said: "Unfortunately there is always going to be a rough patch to go through.
"Second place? I have always said the goal is to finish within the first five places and we have more points than last year. But I think the glass is half full and we cannot admit defeat yet."
The former Sampdoria coach also slammed the fickle nature of some sections of the Italian media for criticising his defence in the aftermath of Sunday's defeat.
Mazzarri added: "Until yesterday we were talking about an impenetrable defence, but today it is believed we have some problems defending."
Napoli continue their pursuit of Juventus with the visit of Atalanta to Stadio San Paolo next Sunday.