It was the second Cup elimination in a week after their Carling Cup exit at Blackburn Rovers, but Moyes insists: "We have had tough tests - all managers face difficult times, and I have had some.
"No-one has a divine right to win football games. You have to earn the right to do so.
"Managers can get into situations where it can be hard, and I have had it before. That's your job.
"There's no manager in football who thinks they have an easy ride, that's for sure. That's part of it. But I want to stay."