The champions' loss to West Brom on Saturday saw them slip to 12th in the Premier League table with a return of just seven points from their opening six games.
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"I've been in situations very similar to this at my old clubs - Everton and Preston North End," Moyes told reporters.
"[To get out of it] you do the right things and I haven't changed what I've done. You continue to do the things and the results will come, there's no doubt about that.
"[Rotating players] never caused Sir Alex Ferguson any problems. Manchester United have always had big squad of players and it's my job to use them and find out what is suitable. And, as I said earlier, I'm getting to know them much better."
Robin van Persie was on the bench for the weekend loss and Moyes says that his star man could start in the Donbass Arena after recovering from a thigh injury.
"He's fit," said Moyes. "We'll make a decision [on Wednesday] on whether we start him.
"He's as good as anybody I've seen. His movement and his football common sense on the pitch is fantastic, as well as the positions he picks up. He's a great goal scorer. He scores all types of goals."
Moyes travels to Ukraine looking to open up a gap at the top of Group A against Shakhtar and, ahead of the clash, the Scot has revealed his long-term aim is to win the Champions League with United.
"I said to win the Champions League you need a certain amount of world-class players," he continued. "That's something we'll try to do. Of course we'll try to win the Champions League - that's part of the job at Manchester United and that's something I'll try to make happen."
"I'm looking forward to [facing Shakhtar]. "It's a game between two teams who have started the group well. It's a difficult place to come and play. They've got a very experienced coach, but I'm looking forward to it.
"We'll be looking for a balance of experience and youth. We'll try to introduce new young players at the right times but also rely on the great experience many of the players have at Manchester United."