Having fallen behind to Lorenzo Insigne's strike 39 minutes in at Stadio San Paolo, Giacomo Bonaventura hit back before half-time to earn Milan a share of the spoils against their title-chasing hosts.
Napoli enjoyed long spells of possession but failed to get the winner that would have returned them to the top of the table, as a dogged display from Milan extended their unbeaten run in the league to seven matches.
That spell includes draws with Roma and Napoli as well as wins against Inter and Fiorentina, leaving Milan sixth - eight points off third place.
"After seven games unbeaten, even against teams like Fiorentina, Inter and Napoli, we too can fight for third place if we keep up this form," Mihajlovic told Mediaset Premium.
Milan had to survive plenty of Napoli attacks and the hosts had great chances to claim the points late on, including a Dries Mertens effort that struck the post.
"It was an extremely difficult game in a stadium where it is almost impossible to win," added Mihajlovic.
"Napoli dominated the game and took the initiative, as they had to, while we tried to hurt them with as many counter-attacks as possible.
"This is the way we had to prepare the game, as we could do nothing else. We need more character and determination but I compliment the lads because they are becoming tough, the way I like them."