United won 3-2 at Villa Park, coming back from two goals behind to grab the win in the closing minutes through Javier Hernandez.
"Absolutely magnificent result for us, it is a magnificent game I must say that," Ferguson told Sky Sports.
"Aston Villa have done fantastic today, they have run their socks off, and you have to feel sorry for them the effort they put in, but we never gave in and hit the bar twice in the second half, but once we got the second goal we came alive and it was a fantastic game."
Ferguson admits his side were told at half-time they needed a big improvement, adding: "They were careless in the first half and there was no real tempo to the game, not a shot on goal and they had to improve on that and they did.
"We have put pressure on ourselves today but we came through it and that is a lesson that we really need to be better in defence.
"You admire the tenacity of the performance when they need to do it, they do it and the attacking play was terrific at times."
Ferguson was full of praise for Hernandez who came off the bench to claim the match ball.
"He does his natural thing, he is fantastic in the penalty box, his movement, his quickness and being in space has got him three goals today," he continued.
"I have said in the last weeks he is fresh after a good summer break and that has made the difference. When he came two years ago that is what we saw."
Ferguson admitted Hernandez was now set to start against Norwich City next week.
"When you score a hat-trick you pick yourself and I think he will be playing next week," he said.
Wayne Rooney went off late on and is now a doubt for England's friendly with Sweden with an ankle injury.
"He has an ankle knock, he has ice on it and we will see how he is tomorrow," he said.