A 20-year-old fan has been arrested and bailed on suspicion of racially abusing Adeyemi towards the end of the two sides' FA Cup third round tie.
"Whatever the outcome of what is now a police investigation, all of us are deeply sorry for what happened on Friday night and our players and our Club pass on our sincere regrets to Tom Adeyemi for the upset and distress he suffered as a result of the matter at hand," read the statement.
"Our supporters are renowned throughout the world for their outstanding commitment, passion and fairness. They are drawn from nationalities across the globe with widely diverse backgrounds and heritages. The actions of any one individual do not represent our fans. Their stance on these issues is just as resolute as the Club's.
"Regarding the incident that occurred on Friday evening, we have given Merseyside police every possible assistance we can and will continue to provide the necessary support to their investigation in order to ensure this particular incident is dealt with properly. We will continue to take the strongest possible action(s) against unacceptable behaviour during our matches."
Liverpool striker Luis Suarez was recently banned for eight matches by the Football Association for racially abusing Manchester United defender Patrice Evra during a game in October.