The English champions have endured their worst start to the season since 1989 and are in the bottom half of the table in 12th with seven points after back-to-back league defeats against Manchester City and, more surprisingly, West Bromwich Albion.
"I have been in situations very similar to this at my old clubs Everton and also at Preston. You get on and you do the right things," Moyes told reporters before his side secured a creditable 1-1 draw against Shakhtar Donetsk in the Champions League on Wednesday.
"I haven't changed what I have done. I will continue to do that. The results will come. I have no doubt about that.
"It is always the thing at Manchester United - everyone is interested in them. It is a talking point for everybody throughout the world," added the Scot who has not been far from the back pages of British newspapers since taking over from Alex Ferguson.
With boos heard around Old Trafford at the end of the West Brom defeat, United fans may think they have got it bad but next up for Moyes's men is a trip to bottom club Sunderland, who sacked coach Paolo Di Canio last month following a string of poor results.
Whatever the result on Saturday, Moyes is unlikely to suffer the same fate any time soon, according to former United defender Gary Neville, now a pundit for Sky Sports.
"David Moyes will be given time over three or four years to build a football club and learn the ropes. It takes time and he'll be given time, just as Arsenal have done with Arsene Wenger," said Neville, who retired as a player in 2011 after almost 20 years at the club.
"If you think about the early years of Sir Alex Ferguson, he was allowed to develop into a presence. In the first three or four years he was at the club he was coming under intense pressure.
"David Moyes, there's no doubt about it, is still learning to come to terms with his squad and getting to know his players and the culture of the club," he added.
On Sunday, West Brom host league leaders Arsenal, who have been rejuvenated since the arrival of Mesut Ozil from Real Madrid on transfer deadline day.
Arsenal are unbeaten in 10 games in all competitions and the Germany playmaker was central to the Gunners' 2-0 win over Napoli in the Champions League on Tuesday, scoring his first goal for the club.
"He enjoys playing football, he enjoys playing with his partners," said Wenger. "Of course he has given everyone at the club a lift and belief, and belief is a part of the success of football."
Liverpool, two points behind the leaders, host struggling Crystal Palace on Saturday boosted by last weekend's goalscoring return of striker Luis Suarez against Sunderland after a 10-match ban for biting Chelsea's Branislav Ivanovic.
"He's just given us more confidence," team mate Lucas Leiva told the club website (www.liverpoolfc.com).
"The squad that we had without him was a good one, but with him back in it, we'll be even better. He's one of the best in the world."
Seventh-placed Manchester City, who have yet to win in the league away from home after losing 3-2 at Aston Villa last time out, return to the Etihad Stadium to face Everton on Saturday.
City will be looking to rebound after suffering a humbling 3-1 defeat at home to Bayern Munich on Wednesday as last season's Champions League winners handed out a masterclass in possession football.
Chelsea travel to Norwich City on Sunday without striker Fernando Torres, who was already suspended for the match but limped off with a knee injury during the 4-0 win over Steaua Bucharest in the Champions League midweek, and Tottenham Hotspur, in third, take on London rivals West Ham United.