The score line could have been much bigger had United taken more of the chances they created and had Wayne Rooney not missed a penalty in the first half.
The score in reality could have been 4 or 5 to the home side if they had taken more care in front of goal.
"I was disappointed to be honest with you, [it was a] game where we should have won by four or five," the Scot told reporters after the game.
"I think I need to sleep on it, I could not believe the chances we missed.
"We should have put it to bed a long, long time ago and you look at that score line 2-1 and you think it was a close game, but it wasn't a close game.
"I think there was a lack of urgency in our game throughout, far too casual. It was an unusual Manchester United-Arsenal game really."