Despite having the majority of possession, United struggled to carve out many clear-cut openings and went down to Anthony Pilkington's header on the hour mark.
"You've got to give credit to the way Norwich defended - they defended for their lives tonight," said the Glaswegian boss afterwards.
"The only chances we had were half chances. Their goalkeeper (John Ruddy) had a good night too. We had a lot of pressure but didn't get the goal we needed."
Defeat for United meant that their Manchester rivals City usurp them atop the Premier League.