Shakhtar Donetsk forced a goalless draw against the Italian side in the second game Champions League Group B encounter on Tuesday evening.
Milan had possession of close to 60% but could not break resilient Donetsk who now remains at the top of the group with 4 points.
It was a slow start for both sides but Milan got an early corner that yielded nothing before another set-piece on the left-wing. In the 15th minute, the hosts were forced to an early change Dentinho was brought in for the injured Taison.
Milan continued to push for an opener with Lautaro Martinez's header from the center of the box being saved by the goalkeeper. Lukaku got another chance minutes later but his effort from the left side of the box was saved by Anatolii Trubin.
The result means Milan is yet to win in their last two matches having settled for a 1-1 draw with Lazio in the group opener. Meanwhile Donetsk with four points.