Heavy home defeats against rivals Liverpool and Manchester City in recent weeks have seen the Scot's position come into question, with United sitting seventh and 18 points adrift of leaders Chelsea.
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When whether he had the full support of his squad, Moyes told reporters: "Definitely. No reason to suggest anything else.
"They’re great, they train great, we work well together and we have a great relationship as far as I’m concerned. But what I want is for us to have a winning team, me and them together.
"The players know exactly what it is to play for Manchester United and the standards they have to set.
"But they're hurting as well as me and are desperate to put it right. And hopefully when we get to the game against Villa, they can show that.
"It's a long journey here and this is only the start of it. You work hard to get here in the first place but I've got to say I'm more driven to succeed than ever.
"I want the team to turn around and I want to change the position we're in just now. I really do believe we can do that.
"We’ve got a great club, which gives you the chance to do that because of the people we can attract and the players we can attract to the club. But it’s just going to take a little bit of time to get it sorted."