The Magpies won 1-0 at Old Trafford on Saturday, compounding Everton's midweek victory, to leave the Red Devils languishing in ninth in the Premier League.
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"It's difficult for David and the club at the minute - they've had some tricky results," the Newcastle boss remarked to BBC Sport.
"He's a great manager. It's very important now that the fans of Manchester United and the board stick with him because he's already proven he's going to be great for this club but it is some sticky days; we all have them.
"David might need a year like that when it's touch-and-go but he'll get it right because he is a strong man," Pardew added. "I have a great respect for him.
"He had a bad break [on Saturday] with Wayne Rooney being unavailable because he'd been in top form."
Moyes himself feels that there was not much in either defeat and is confident that his players can bounce back, while condemning reports of a falling-out with star striker Robin van Persie as "absolute nonsense".
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"We have to play better, pass it better, make more chances, take the opportunities when they come and we've just not been able to do that in the last couple of games but the players give me the confidence we can still be in the mix at the end of the season. They are the Premier League champions.
"I don't think I've changed anything. It's the same players," Moyes replied when asked how much his influence had affected the team's fortunes.
"I've brought one player in [Marouane Fellaini] and I'd have done that anyway. If I'd changed it, there might be something to be critical of but we've gone along with basically the same players and introduced young Adnan Januzaj into the team, so I don't think we've made any changes."