United were already trailing by two goals until Rafael da Silva, on as a substitute, volleyed home a late strike, but it was too little, too late.
"The chances we had in the game were incredible," Sir Alex Ferguson told Sky Sports. "It was the area in which we let ourselves down. I think if we'd got one when Ronaldo got his great chance, then we'd have got something out of the game.
"It was fantasy football, it was like playground stuff - you attack, we attack - and they got the goals that mattered. In fairness to my own team, after the second goal their determination and drive to try and rescue the game was fantastic, and we probably deserved something from the game, I think."
The United boss felt the whole affair was a tremendous advert for attacking football.
"Some of the football out there today from both teams was magnificent," he said. "I don't think you'll see a game as good as that anywhere else in the country.
"Sometimes you just have to hold your hands up and say 'if you're going to get beaten, just make sure it's someone who's going to play football', and Arsenal played good football at times. Not as dangerous as us in attacking play, but they got the goals that mattered."