The Scottish giants dominated much of the play at the San Siro in their Champions League opener but in the end came up short as Cristian Zapata's deflected shot in the 82nd minute and Sulley Muntari's finish from close range minutes later gave the Rossoneri all three points.
Although Celtic were beaten, it was an impressive display which just lacked some efficiency in front of goal which was acknowledged by midfielder Brown.
"I think we played really well, we created a lot of chances and overall, I thought we were the better team," he told Sky Sports.
"They got a lucky break and scored the first goal and we were always going to try and push forward.
"We knew we were going to get possession, we knew we were a good team and I think we gave just as well as we could give.
"We had a lot of chances and a lot of possession as well. We played well as a team but sometimes playing well doesn't get you anywhere and there's always the rematch."
Brown was already looking to the November return bout when Milan head to Glasgow: "We knew it was going to be a tough group, it's going to be a tough group for everybody, not just us. They've got to come to Celtic Park and it's going to be harder."