Massimiliano Allegri's side was frustrated at lowly Sampdoria, as his forwards failed to find the cutting edge required to put go ahead.
Youthful vibrancy seemed to be the aim for Milan, as M'Baye Niang was given his first Serie A start for the Rossoneri, with the 18-year-old Frenchman partnering Stephane El Shaarawy and Bojan Krkic in attack.
After a composed start, Lorenzo De Silvestre fired the first warning shot of the game in the sixth minute, unleashing a venomous drive at Cristian Abbiati in the Milan net. The veteran shot-stopper got down well to beat the strike away from danger, athletically preventing his side from conceding an early goal. The 35-year old was called upon again minutes later, turning two more Sampdorian efforts from Eder over the bar, as the home side pressed.
In the 20th minute, Daniele Gastaldello found himself kicking Abbiati's post in frustration, after the Sampdoria defender failed to turn a header home, from what looked like a somewhat easy opportunity.
Milan's first real chance of the game fell on 33 minutes, mercifully giving the Sampdoria's Sergio Romero something meaningful to do. A long-range Ricardo Montolivo strike was the best effort that the visitors could muster in a sluggish first half performance, as the Rossoneri struggled to impose themselves in Geneva.
Misery for the visitors was compounded just before the break, as Bojan blasted a shot wildly over the bar from 30 yards, and Milan's young forwards looked to be visibly aging as a result of their torrid first half experience. For those in red and black, the referee's halftime whistle was welcomed.
The second half began in a totally different vein to the first, as Romero was forced into action from the off, turning a Niang effort acrobatically over the bar - following a cheeky nutmeg from the Frenchman.
Cristian Zapata almost grabbed a goal for Milan at the wrong end moments later, deflecting a Eder strike just past the post, leaving Abbiati helplessly rooted to the spot, as what had previously been a dull game seemed to turn on its head.
Following Milan's resurgence, the home side held on desperately, counting upon a 61st minute goal-line clearance to deny out-of-sorts Kevin-Prince Boateng from turning home a back post cross, after good work at the line by Niang.
Merely two minutes later, a Mauro Icardi effort beat both Abbiati and the frame of his goal, and with such wastefulness on display, it seemed evident that the match would be heading towards stalemate.
Milan's Robinho was thrown on by Allegri in place of El Shaarawy as a potential catalyst, as the game remained in the balance, but neither side could take their chances.
In the later stages frustration was shared, as neither side could find the back of the net nor the quality to create chances, through goalkeeping brilliance or a sheer lack of quality when it counted, as time petered out.
Young Niang provided a welcome injection of spark and creativity for the visitors, who will need to improve hugely for their next fixture, while Sampdoria snatches another welcome point.