Inter went ahead in the 16th minute when Ricky Alvarez showed neat control before finishing coolly, but Atalanta responded through German Denis who produced a characteristic striker's header to level the scores in the first half.
"In my view we deserved to win," Mazzarri told Sky Sport Italia. "If you look at the scoring opportunities, then we created more than Atalanta this evening, especially in the second half. We need to be more clinical and sharp in attack.
"We also have to improve our attitude and score more goals in this period that we're missing Diego Milito. We were naive to give away a goal when in front. We have many aspects to improve upon in order to battle for the top spots.
"Atalanta are a strong side and I complimented Stefano Colantuono. Denis is one of the best centre-forwards in Italy. He didn't play that much for me at Napoli, but when he did he was always ready. Now he has consistency, regular playing time and therefore more goals."
Inter now find themselves fourth in Serie A having played one game more than most other sides in the league.