Moyes's United were booed off by sections of the Old Trafford crowd after losing 1-0 to Newcastle on Saturday afternoon.
The Red Devils, who have now lost back-to-back Premier League home games for the first time since May 2002, remain ninth in the table.
Their chances of being crowned English champions for a sixth time in eight years look very slim, as reflected by bookmakers BetVictor, who are offering odds of 33-1 on such an occurrence.
Despite Man United's poor start under Moyes, Pardew is convinced that the Scot will produce success at Old Trafford if the supporters remain patient.
"I think it is difficult for David and the club," Pardew told reporters. "He is a great manager.
"It is very important the fans and the board stick with him. He has proven [with his performance as Everton boss] he will be great for this football club. David is big enough to stand up [to this challenge]."
Man United are next in action on Tuesday night when they host Shakhtar Donetsk in the Champions League.