Mazzarri had targeted a Serie A victory in Bergamo on Tuesday, but his players failed to make the most of their goalscoring opportunities and had to settle for a point.
"I'm not sure the draw was a fair result," Mazzarri said. "Atalanta are a good side but I believe we should have won.
"We were naive in certain situations and we lacked the killer instinct. We should have done better."
Inter have won just one of their last five games and Mazzarri admits the absence of injured striker Diego Milito is hurting his side.
The Argentina international has been out of action since sustaining a left thigh injury on October 5.
"We are without our reference player in attack," Mazzarri said, according to Gazzetta dello Sport.
"We miss Milito and perhaps had he played alongside Rodrigo Palacio, the result would have been different at Atalanta."
Milito is unlikely to recover in time for Sunday's game at Udinese.
Inter stand fifth in Serie A, one point clear of Fiorentina, who take on Napoli on Wednesday.