The Scot has won just two of his first six games since replacing Sir Alex Ferguson in July and faces Sevilla in his final pre-season game ahead of Sunday’s Community Shield.
Moyes has, thus far, been frustrated in the transfer window - attempts to sign Thiago Alcantara and Cesc Fabregas from Barcelona have floundered, while the ongoing speculation surrounding Wayne Rooney’s future clouds United's off-season preparations – and he notes the "step up" from Everton has been a reality check.
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"Everton are a great club and I was proud to manage them. I can't deny Manchester United is on another level. Let’s be honest, it would be a step up from just about any club in the world. The level of interest from the fans and the press is phenomenal."
United will face Chelsea, Liverpool and cross-city rivals Manchester City in their opening five games of the Premier League season - a fixture list that Moyes has admitted to being suspicious of - but he is excited at making his competitive bow in Old Trafford hotseat.
"I cannot wait to get the season started," Moyes added. "I know what it’s like to step out at Old Trafford as the manager of the opposition, so to step out in front of 75,000 fans as the Manchester United manager will be special for me.
"I know it won’t always be easy, but I just hope we can all work together. My sole goal is to be successful and have a winning team. I hope that over the years we can have plenty of success."
Moyes' first test will be facing FA Cup winners Wigan in the Community Shield and, while he feels any potential victory will be an extension of Sir Alex’s 26-and-a-half year reign, he hopes to kick-start his own tenure with a victory.
He continued: "Of course I will be trying to make the Community Shield the first trophy of many, but if we win it's really something that will have been earned by Sir Alex.
"It's because of his good work in the Premier League last season that we’re in the Community Shield. I'll do my best to finish off the job, but it’s Sir Alex who will deserve a lot of the credit if we’re successful."