Goals from Anderson and substitute Danny Welbeck in the final quarter of the match gave United a club record 19th successive home league win, but it could have been so different had the Canaries taken their chances.
“Norwich set out their stall very well in terms of two central midfield players staying in front of the back four and any system like that is hard to break down,” said Sir Alex.
“Every counter-attack they had, they got something out of it – they played long balls up to the centre-forward, Morison, and they played off it very well and hit the post, and had a great chance to go 1-0 up and that’s what happens when you’re playing a counter-attacking game.
“You have to be really clever defensively to deal with it.”
He admitted his players were below their best but applauded their perseverance.
“This was not a good performance but we were gritty and we never gave in. That is a fantastic quality to have,” he said.
“I thought we were far too slow on the ball in the first half. We changes things round a little bit in the second.
“Once we quickened the game up in the second half we were much better. We deserved to win because we kept at it in our own fashion and we never gave in.”