The Netherlands international feels a combination of inexperience and bad luck contributed to his side's 3-0 defeat at San Siro on Wednesday
The Eredivisie giants were beaten 3-0 at San Siro on Wednesday after they were held to a 1-1 draw in the first leg at home, yet Bruma feels his inexperienced side were a little unlucky not to have progressed to the group stage.
"We lacked the killer instinct that Milan have and that's why they won. I think experience made the difference. They had four or five chances and scored three goals – this is the killer instinct that we don't have yet," Bruma told the official Uefa website.
"It was a good experience and we had a chance to go through as well. In the first game we were no worse than Milan and also Wednesday I think if we had made it 1-1 when we had the chance it would have been a different game.
"Then they made 2-0 and the game was nearly over. Obviously at this moment we are a bit angry but now we have to go on with the Europa League and give our best there."
Milan have been placed in pot two for Thursday evening's Champions League draw in Monaco, which takes place at 17:45CET.