A group of disgruntled fans carried out their threat to fly a protest banner over Old Trafford.
A plane buzzed over the ground for the first 10 minutes of the match with the message 'Wrong One - Moyes Out' behind it.
Former United defender Gary Neville said the protest lacked class and most of the fans inside the stadium agreed. There were boos and songs of support for Moyes as the plane hovered above the stadium.
"The support inside Old Trafford has been terrific and if ever there was a show of support for their football club and for their team, it was today," the United boss said.
"Inside Old Trafford it was terrific, it really was."
Moyes said he took no notice of the plane.
"I was concentrating on the game," he said.
The United manager, who has lost six home games this season, was pleased to see the response from the crowd.
"I just wanted everybody to know that I am the manager of the club and you know where I am," he said. "I stand on the edge of the pitch every week. That's my job."