Morrison has become a first-team regular this term under Sam Allardyce, and he has taken his opportunity with both hands.
Morrison sealed West Ham's shock 3-0 win at Tottenham with a brilliant individual effort.
"He deserves all the credit he is getting at the minute," Noble told Sky Sports.
"There has been a lot of hype about him in the last few years and is he going to fulfil that potential? At the minute he is because he is working hard and his discipline is right.
"There are a lot of senior players at this club and I know I am on him to do things right, and the skipper [Kevin Nolan] is and the gaffer has sort of taken him under his wing, and he is becoming a man now and deserves his place in the team."
Noble feels the fact Morrison has settled so well in the capital is a big part of his current form.
"He is enjoying London, his family is in Manchester and is close to him, but he is enjoying where he is living and enjoying coming in and we are looking after him and if he continues like that I am sure he will go far in the game," he said.
Stewart Downing added: "He has been at it from the first game, since I came in pre-season.
"You can see he has got ability, two feet, can score goals and can see a pass, and you can see from his finish to do that here."
Manager Sam Allardyce labelled Morrison's goal as a piece of 'genius'.
"That is a genius goal for me and you will struggle to see a better one this season.
"There is a lot of praise that will come his way and deservedly so after that goal."
Allardyce admits that Sir Alex Ferguson pushed him to keep persevere with Morrison - who spent last season on loan at Birmingham.
"Sir Alex said: 'I hope you can sort him out because if you can he will be a genius. He needs to get away from Manchester and start a new life'," Allardyce revealed.