The 20-year-old scored twice for the England Under-21s on Tuesday evening as they defeated Lithuania 5-0.
Allardyce has stated that he is looking to aid Morrison's development as a footballer.
"I have to be careful with the amount of publicity that Rav gets," Allardyce told The Independent.
"To make sure that we just continue his growth slowly and continue him playing in the team to the level he's playing and try to get him better and then there is no distraction that might put a young man off at this stage of his career, which can happen.
"They can have their ups and downs, they burst on to the scene, they can get lavished with praise and then lose their focus and, when they lose their focus, they can dip away again, and I don't really want that."
England boss Roy Hodgson has admitted that he is monitoring Morrison's progress.