Chelsea and England captain John Terry was charged by UK police after allegedly making racist remarks to Queens Park Rangers defender Anton Ferdinand in October 2011.
The court heard how Ms Musa, from Darfur, Sudan, and her friend Mary Marandran, from the Congo, were sitting on a bench in a play park when they heard racist phrases.
The court heard Barton had shouted racist abuse at Anthony as he waited at a bus stop near the Huyton Park pub with his cousin Marcus Binns and girlfriend, Louise Thompson.