United face Chelsea on Monday night in Moyes' first Premier League game at Old Trafford since replacing Sir Alex Ferguson.
Despite opening their campaign with an eye-catching 4-1 win at Swansea, and seeing major rivals Manchester City surprisingly beaten at Cardiff onSunday, there remains an air of negativity surrounding the club.
With no new signings and Wayne Rooney's future remaining uncertain, many outsiders wonder if United will have the durability to resist a challenge from Chelsea boss Jose Mourinho in particular.
Moyes expects the response to be a positive one.
"We are getting written off quite often," said the Scot. "In the main, when that is the case, this club tends to say 'we'll show you'.
"It is in my nature. It was definitely in the previous manager's nature. And the supporters here understand that as well."
That United have been able to post what they claim to be a British record 63,000 season ticket sales underlines that their fans remain solidly behind Moyes.
And veteran defender Rio Ferdinand has been around long enough to be convinced about United's abilities, regardless of how the short term results over their hazardous start to the campaign turn out.
"That run of fixtures is good for the media. It makes a story," said Ferdinand. "When I first looked at them I thought it is a tough start for the new manager. But it is an exciting start too.