Goran Pandev cancelled out Mathieu Flamini's opener to keep Napoli four points ahead of Milan in second-place.
“We haven’t achieved our target of Champions League qualification yet, so we mustn’t let anything go,” Mazzarri told Sky Sport Italia.
“I am not remotely satisfied with the result, as we pegged Milan back in their own half and I really hoped to win this game. Looking at the incidents, we deserved a victory.
“Towards the end, when Milan went a man down, I really saw us coming away with all three points, but we weren’t clinical enough. We always allow our opponents more chances than we should.”