The Scotsman has been under scrutiny since taking over from Sir Alex Ferguson at Old Trafford in the summer.
The Red Devils slipping 13 points behind leaders Arsenal in the Premier League table, and Moyes has taken the brunt of criticism.
"I think people are getting carried away with where they are in the table," the Daily Mail quotes Moyes as saying. "They are still a very good team.
"Let's face it, any manager going in there would have found it hard. So I think the criticism David has received is over the top."
United will travel to the Midlands to take on Villa on Sunday.