The 20-year-old from Aintree, Liverpool was arrested after match officials made a complaint to Merseyside Police after the FA Cup third-round fixture on January 6.
Adeyemi, 20, alleged a fan had shouted a racially abusive comment at him as he retrieved the ball from near the crowd.
The CPS said that after police interviews with the footballer and the suspect, and viewing "enhanced" CCTV footage, there was insufficient evidence to bring any criminal charges.
In police interviews, the man admitted shouting at the player, but denied it was of a racial nature. Witness statements from others in the crowd "tend" to support the man's version of events, the CPS added.
Source: AFP