Arsenal have not beaten Manchester United since the early part of the 08/09 season.
Today, Alex Ferguson fielded a weak side. The weakest United side Arsene Wenger has ever faced (not including a League Cup match years back). Arsenal were missing players but were much closer to what may be called "full strength". United ran out comfortable winners nonetheless.
Even if Arsenal pull themselves together for the remainder of the league season, much will likely rely on the game between the two teams at the Emirates. United will not be playing full backs on the wings, centre backs in midfield. We can't predict their line up but we can predict the way Arsenal will approach the game. United have got so used to it that it seems Ferguson can beat Wenger using any kind of starting eleven.
Arsenal are not that good, unless the object of the game is to play well between the two penalty areas. Against Barca, the pressure was so great that they failed even to do that. Against United, they were allowed to do it. United settled for winning the mini-games in both penalty areas. That was enough. In the space of a week, Arsenal have fallen foul of the best midfield in the world, and then no midfield at all.