The win lifted the Orobici into 10th place but Mazzarri's men slip to third, six points behind leaders Juventus, following their second defeat in three games.
The 51-year-old coach claimed the Partenopei deserved to win on the balance of chances created.
"We allowed only one scoring opportunity and they found a great shot," the ex-Sampdoria manager told reporters.
"We had seven or eight shots on goal but the Atalanta goalkeeper performed some stunts that eventually enabled them to win.
"On the whole I am satisfied with the team. Compared to last year we have seven more points, we are growing and we can certainly improve even more."
Edinson Cavani, one of Napoli's chief sources of goals, is nearing a return from injury but Mazzarri said the Uruguayan admitted before the game that he was not quite ready to return to the team.
"Edi is not fully fit. I gave him carte blanche to choose, but he did not want to go onto the field [tonight]."