The Tottenham Hotspur defender, who is currently on loan at Sunderland, stormed off the field at the end of England's late 1-0 win over Serbia in their European Championship qualifying clash on away turf last night.
"When we went out for the warm-up on the opposite side of the bench they started monkey chanting straight away," Rose told Sky Sports News.
"Halfway through the warm-up I went to the assistant manager (Steve Wigley) and I told him what was happening. He said I should try my best to get through it and we'll deal with it after the game.
"The first half was no way near as bad as the second half. I had two stones hit me in the head when I went to get the ball for a throw in. Every time I touched the ball I heard monkey chants. After 60 minutes my mind wasn't really on the game after that, I was so angry. I don't understand how they can learn from it, they have to be banned."
England reported the incident to UEFA following the match.