By Tom Hayward
The build-up to the game was dominated by the decision of some disgruntled United fans to charter a light aircraft that trailed a banner reading 'Wrong One - Moyes Out' overhead as the match started.
In an unusual act, Moyes appeared from the tunnel before the teams and received a rousing reception from those inside the stadium as he made his way to the bench.
"I've been saying all the time since I've been here the crowd have been great," Moyes told BT Sport. "They've been terrific to me because at times we've not done as well as we like.
"Right from the start we didn't start the game well but I've got to say the crowd were brilliant in getting behind the team. The crowd inside Old Trafford today really showed up."
Moyes' team have endured a lacklustre season, languishing in seventh place in the table, 15 points behind leaders Chelsea and nine behind fourth placed Arsenal. Both have a game in hand.
Before the game, Moyes told reporters that even his predecessor Alex Ferguson would have struggled as manager of Manchester United this season.
The 50-year-old is focused on adding players to what he believes is already a strong team.
"When I came in I knew exactly what the task was going to be. We have to build a team here. I've already got a good team here, I took over the champions from Sir Alex. It was a great team.
"Now there's time where we need to try and add to that. All the players I seem to talk to seem to want to join Manchester United and hopefully that comes to fruition in the Summer."
Wayne Rooney, as he has been for much of the season, was the main man for United and scored two goals after they had conceded an early Ashley Westwood goal.
January signing Juan Mata scored his first goal for the club before substitute Javier Hernandez added a late fourth.
"He is a top player. He's been great since the start of the season," said Moyes.
"Anything I say I'd only be repeating myself but I did say to him after the game: 'If you keep scoring two goals a game for us it's going to give us a great chance of doing much better'. His form and the way he's been playing has been very very good."
It was the second successive game in which Aston Villa scored an early goal before going on to lose 4-1.
"I didn't think there was too much in it to be honest. 4-1 is pretty harsh on us," Villa manager Paul Lambert said. "When you come to places like this you've got to take your chances when you get them." (Reporting By Tom Hayward, editing by Alan Baldwin)