The Everton boss, who will replace Sir Alex Ferguson at Old Trafford from July 1, was viewed as a surprise appointment by some given his lack of experience at Europe's elite level but feels that the United job is simply the next challenging step up on the managerial ladder.
"There's a real spotlight on me right now and the pressure that comes with it but, when you're a young manager, you dream about that, about getting as close to the top as you possibly can," Moyes told the press. "It's what you are aiming for.
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"I see them just as steps up and that is what you want, to keep progressing, to aim for the top and what comes with that. The key is to keep yourself focused, to shut yourself off from the pressure and get on with your job."
Another question mark over Moyes's suitability as Sir Alex's successor has been his playing style, with many, including Steven Gerrard earlier in the season, labelling Everton a long-ball side under the Scot.
The manager rubbished such claims, however, claiming that his team's style has improved over the years in relation to their relative financial constraints.
"I hope and I believe that the style of my team has evolved over the years; I think we are playing a brand of football that has evolved into a better style," he insisted.
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"At Everton, we have played football that I'm proud of, that I would have paid to watch myself, but we have also had to find a way of winning when we haven't been able to compete financially with the top clubs at times and, for the most part, we have achieved that."
Despite admitting he was never tempted to stay at Everton once he was offered the United job, Moyes added that he will leave Goodison with a heavy heart.
"Everton's such an important part of my life, so of course it is incredibly hard to walk away from this great club and the great people here," he added.
"I have to be honest – and I always try to be – I would have to say that, no, there wasn't any part of me that thought about staying at Everton but an awful lot of me knows how difficult it is going to be to leave.
"I have immense respect for the chairman; he gave me my chance and I can honestly say he backed me every single step of the way.
"The chairman has asked me about a successor and I will do whatever I can to help him."