Gary Deegan's goal booked a quarter-final date with Kilmarnock for Hibs, but Aberdeen will wonder how a late siege failed to yield a goal.
Ben Williams pulled off save after save, none more impressive than the one which kept out Scott Vernon's penalty.
Brown's side have now scored just once in four games, and the manager said: "I'm quite mystified as to why we're not still in the cup.
"The team played with enthusiasm and fought to the bitter end. We didn't deserve to lose the game but we're not scoring.
"You can't get better chances than a penalty kick. I don't think Scott Vernon has missed a penalty kick before."