It is not so much a fear of failure for a man who in more than a decade at Everton did not win a trophy, rather the stature of the 20-times English champions and the huge success of his long-serving predecessor Alex Ferguson.
"There has to be an element of fear that comes with managing a club like Manchester United. It keeps you working, it keeps you focused and helps you try not to take your eye off the ball," British newspapers quoted the Scot as saying.
"You would have doubt if anybody took over this job, but in my own way, I've got to say I feel it's the right job for me at the right time and hopefully I'll make it work."
Moyes took up his post at the start of this month and his first games in charge have been on United's pre-season tour of the Asia-Pacific, where they have lost one match and won the other so far.
The 50 year old, who was handpicked for the job by Ferguson, has often said he will call on his predecessor for advice but also emphasises that this is a new period for the club.
"It has to be a new era," he said. "Whatever we say, my job now is to make my history.
"I'm going to follow someone who has made incredible history. I think about Matt Busby's history and then Alex Ferguson's history – they could do a film about it.
"I have to make sure now that my history and my time is something which the fans and people in the future talk about."
Moyes' start to his tenure has been trickier than it might have been as he has grappled with a barrage of questions surrounding the future of striker Wayne Rooney from the first day.
Repeating the club's "he is not for sale" mantra, Moyes has nevertheless steered away from saying the England international has changed his mind about wanting to leave the club.
Rooney's early departure from the tour because of injury has only fuelled media speculation that he is on his way out, with Chelsea saying they have made a bid for him, and United's pursuit of Barcelona's Cesc Fabregas has fanned the flames.
The new era that Moyes is talking about seems to be manifesting itself in their approach to transfer targets with the club ditching its traditionally more secretive handling of matters to openly say they are trying to sign the Spaniard.
Where the United website would usually only announce a new arrival when the player had signed on the dotted line, this week it has carried an article headlined 'Second bid for Cesc' with Moyes himself confirming a second offer.
Bringing in Fabregas would reunite him with former Arsenal team mate Robin van Persie who shone last season with 26 league goals as United won the title with a crushing 11-point lead over second-placed Manchester City.
But they may not necessarily get their way with Fabregas' Barca teammate Gerard Pique quoted by British newspaper The Sun on Tuesday as saying the playmaker had no intention of leaving the Spanish champions.
"United are wasting their time," the defender said.
"It took a long time for Cesc to get his dream move back home and he won't give it up. This is home, it is where his family is, and he is playing with his closest friends.
"He has told us he is happy and that he intends to stay with Barcelona."
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