The visitors had the better chances, with Milan's young goalkeeper Gianluigi Donnarumma forced to make superb second-half saves from Luca Cigarini and Alberto Grassi.
Mihaljovic's exasperation spilled over in the dying minutes and he was sent from the touchline after attempting to kick a plastic bottle towards an official, while Alessio Cerci missed a chance in the 93rd minute when he fired into the side netting.
"We were certainly lucky to scrape a point, as we were not the same side that beat Lazio," Mihajlovic told Sky Sport Italia. "This is a Milan with the quality to target our objective, which is the top three."
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The draw leaves Milan in fifth place on 20 points from 12 games, while Atalanta move up to seventh on 18 points.
Struggling Bologna won at Verona, who have six points and are still looking for their first win of the season, thanks to goals from Emanuele Giaccherini and Godfred Donsah.
Giaccherini met Adam Masina's cross with his back to goal and swivelled to send a powerful first-time effort across keeper Rafael and into the far corner of the net in the sixth minute.
They doubled their lead eight minutes later when Mattia Destro's shot was deflected into the path of Donsah, who slid in ahead of Samuel Souprayen to poke home his first goal for the club.
Roberto Donadoni has now won both of his matches in charge since replacing Delio Rossi as Bologna coach on Oct. 28.
"It was important to get a result today and find consistency," he said. "Things are going well, but we must forget the past and build on the positives to move forward.
"The enthusiasm in the squad is reassuring and we
earned these two victories on the field."
Verona remain 19th, level with bottom club Carpi who travel to Sassuolo on Sunday, while victory takes Bologna up to 14th place on 12 points.
There are eight more Serie A matches on Sunday, including the Rome derby between Roma and Lazio, leaders Fiorentina's trip to Sampdoria and Juventus' visit to Empoli.
(Editing by Ken Ferris/Greg Stutchbury)
