Moyes has come under early pressure since replacing Sir Alex Ferguson over the summer due to an indifferent start to the Red Devils' Premier League title defence.
"We're very fortunate that he's our manager, no doubt about that," the 75-year-old told the club's official website.
"Continuity was a big factor in David's appointment. Whenever you change manager, there will, of course, be one or two little differences, but not a lot if you handle it right and we've done that."
United return to action on Wednesday night when they travel to Ukraine to face Shakhtar Donetsk in the Champions League.