Moyes was pleased with how his side found a way to win a gritty match against the struggling Canaries.
"That's six points from two games in three days, both away from home," the 50-year-old Scot told reporters.
"I thought Norwich did terrific today but overall we kept going, we kept at it and we got our rewards in the end. Today we found a way of winning the game despite a lot of injuries and a lot of players out."
United are seven points off top ahead of tomorrow's Premier League fixtures.