Moore said: "I know it's difficult for supporters because they have been watching Ryan longer than me, but there's a new manager (me) in here now who is trying to get the best out of him.
"We need to stick by people and that's why a bit of understanding from the fans could help. It's not nice for him to hear comments from the stands.
"When I was playing, people could scream all day at me and it wouldn't affect me but people have different personalities. Ryan needs a little bit of a hand from the spectators."
Taylor could well still be loaned out to get some goals and confidence in the future but in the meantime will fight for his place in the Millers attack.