Moyes is under increasing pressure after defeat at Stoke City.
Speaking at the launch of the 2014 FA Community Awards, presented by McDonald's, Pallister said: "He will get it right.
"I can understand why people are writing Manchester United off but I am not going to change my mind.
"For me David Moyes was the right man to take over the job. I still think that.
"You have to give him time to understand what the club is all about.
"Sir Alex Ferguson said you have to give him time. Everybody understood that.
"A big transition is taking place. It is not something that is going to happen overnight."