The Scot has the biggest of managerial boots to fill at Old Trafford after agreeing to succeed the legendary Sir Alex Ferguson.
Ferguson transformed United into a global phenomenon during 27 glittering years in charge of the Red Devils.
Ensuring that United remain ahead of their rivals is the challenge now facing Moyes, and he is fully aware of the added pressure he finds himself under after swapping life at Everton for that at the reigning Premier League champions.
He said ahead of an opening day clash with Swansea City, which can be seen live on Sky Sports 1 HD: "Usually you take over because a manager has been sacked or the team isn't doing well. This is completely different because I am taking over a team that's been successful.
"The previous manager has left things in place that are really important. The most important and impressive thing he has left is the winning mentality.
"They have won the league and now it's: 'Lets win the next one'. When you are in there you see it and you feel it.
"The players and their spirit and attitude has really made me stand up and realise and see the difference. I can see the players and the edge and spirit of competitiveness they have.
"But it's a club that has always had to make progress and to change and that will happen with me over the next couple of years or 18 months."
Moyes, who has penned a six-year contract at Old Trafford, added: "My job at Everton was to win but here you have to win even if you're a goal down with two minutes to go. That's why there is a government health warning that comes with this job!
"There is an expectancy and that is to try and win. But I have owners, really good owners, who don't panic.
"They have been fantastic in their calmness, their openness, their support, where they want to take the club.
"We have stability, we know where we are going and how we work, so there is no panic if there is a defeat.
"But I am aware of the job and the job is to continue the success of the club."