Welbeck came off the bench to hit the only goal of the game at Carrow Road.
He told MUTV: "I think it was a very important win for us. Playing two games in three days is really difficult both physically and mentally so we're pleased to get six points over the Christmas period.
"We have gathered momentum, but the most important thing is to look towards the next game because you can't get carried away. The two wins are behind us and we just want to keep winning in the coming games.
"I think during the course of the season, you come across games which aren't pretty, but you have to get a result," he added. "Getting the victory without putting in our best performance is a good sign for us."
Referencing his finish, Welbeck believes there was only ever going to be one outcome when through on goal: "There were a couple of ricochets and thankfully the ball fell for me. I knew that once I was one-on-one with the goalkeeper, I was going to score."
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