"I also thought we should have had a penalty kick because I thought Patrice Evra was brought down.
"But there'll always be controversial decisions in a match like that because there are so many things happening."
Sir Alex felt the performances of United's wingers and strikers were key, although he also had praise for the way his team defended in the derby after lambasting the display at Reading.
"I thought our front four did well in all their different ways," the manager told MUTV. "As I said a couple of occasions back, Wayne needs games and that's why I played him on Wednesday against Cluj. We were hoping that Antonio would be fit, he was touch and go but he wanted to play and showed again what a fantastic asset he is to us. Van Persie kept them on the back foot all the time and I thought Ashley Young played a great part.
"I thought attacking-wise we did very well. And of course after all the controversy about our defending, I thought we defended well today, I really did. City kept fighting, they kept battling and they've got this great record of scoring late goals.
"City scored a second goal and they deserved it. At that point, you're saying to yourself, 'I'll take the draw.' But up to that point, I thought we were far better than them."
Whether United will prove to be better than City over the course of the season remains to be seen. But for now, Sir Alex is happy to have registered an important win in the title race after moving six points clear of the Reds' main rivals.
"When you count the points up in May, I hope it [this win] is significant. Derby games like today are significant if you win them, there's no question about that. I hope it's really significant come