Moyes believes that Hibbert, who has been at Goodison Park since 2002, has improved immensely over time and that Osman has finally made the giant leap to becoming a great Premier League footballer.
"I think he has risen to the challenge," Moyes told the club's official website.
"Hibbo has been one of the ones who has been with us all the way. There is competition and he knows that.
"He is having to keep stepping up to the mark, so does Leon Osman. But those two boys, for me, are part of the brickwork here.
"Hibbo's reliability is the thing. There are some times when we have changed it around. We might have needed a bit better going forward.
"But defensively and in terms of reliability, for me he is someone that you can hang your hat on. The young boys should be looking at him. Hibbo has been great for us.
"He got in at an early age, he hung in there and even when he wasn't getting a game, he was always around the place.
"It's the same for Ossie. He had to go on loan a couple of times early in his career. There are a couple of routes you can take but you have got to keep stepping up.
"When you leave the academy and you come up to train with the reserves, you have to show that you are good enough.
"If you are a reserve team player and you go to play with the first team, you have to show that you should be there.
"What happens as a young player is that you get a little bit of leeway. But eventually you start to get judged like everyone else and you have to keep stepping up."