Swansea City return to Old Trafford for the second time in a week on Saturday, buoyed by their victory at the same ground in the FA Cup third round and no doubt encouraged for another assault by their opponents' ongoing problems.
Sunderland became the latest club to upset Moyes's team in the first leg of their League Cup semi-final on Tuesday, the first time since 1932 that United had lost their first three games of the year.
Yet Moyes, hand-picked by predecessor Alex Ferguson and given the security of a six-year contract, is not panicking.
"I've been here before and done it before," Moyes said on the club website (www.manutd.com).
"I just sense that it's on the verge of turning, we're about to get a bit better. You need a little bit of good fortune to go for you, and it looks as if we're not getting enough of that at the moment.
"I can sense in the dressing-room that there's an urge to fight our current position."
United's fans booed them off the pitch following their cup defeat by Swansea, but it was a different story at the Stadium of Light where they made an effort to rally behind Moyes's cause, singing his name despite their team's limp performance.
Moyes described their support as "exceptional", but is well aware that it is a results business and those in the boardroom as well as on the terraces will soon start demanding an upturn in fortunes.
"If you're going to be in this job you've got to win, and the last few games I've not won," he said.
"It's part of football management. It's never going to be an easy ride. To be the manager of Manchester United is a big challenge, whether it's on the back of wins or defeats."
One thing in Moyes's favour is the congested Premier League table where, despite United's poor form, they remain only five points off fourth place and the final Champions League qualification spot.
All the current top four play away from home this week and the Premier League lead could change hands three times over the weekend.
Third-placed Chelsea can stake an early claim on the summit when they kickoff the action at Hull City on Saturday before second-place Manchester City, who crushed West Ham 6-0 in their League Cup semi-final first leg on Wednesday, travel to Newcastle United on Sunday.
A 3-1 defeat by Villa in the opening match of the season spurred the doom-mongers, who had been prophesying a difficult campaign for Arsene Wenger's team, into overdrive.
However, it preceded their transfer-record signing of Germany playmaker Mesut Ozil and eight wins from their next nine games propelled Arsenal to the top of the standings.
In the five matches at the Britannia Stadium since Stoke returned to the top flight in 2008, the visitors have lost three and drawn two.
Liverpool could be boosted by the return of striker Daniel Sturridge who scored nine league goals before suffering an ankle injury at the end of November.