The Reds conceded an Ashley Westwood free-kick early on but rallied to run out convincing victors thanks to a Wayne Rooney double and second-half goals by Juan Mata and Javier Hernandez.
"We didn’t get off to a great start," Moyes told MUTV. "I think everyone was a bit nervy in that first five to 10-minute period. Once we regrouped and got going, it was good that we got the equaliser and we scored the second goal at a really good time just before half-time.
"I thought the players took the challenge on and rose to it after that and we got better.
"I love my football and the fourth one was a great goal with the interplay on the wing between Adnan Januzaj and Marouane Fellaini and Adnan put in a great cross for Chicharito. It was a goal for a football supporter."
The crowd was clearly supportive from the outset and stuck with the players, even after the Westwood opener. Moyes had made his way to the dug-out before the players left the tunnel for the kick-off and received warm applause from the stands.
"I just wanted everybody to know I'm the manager of the club," he stated. "They know where I am. I stand by the side of the pitch. Ever since I’ve been at Manchester United, I’ve only had support. I don’t where people are trying to change this from but I believe that all Manchester United supporters are behind me and they all understand the situation we are in. The players are incredibly focused, that was an important thing as I wanted the focus to be right.