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The Premier League club have also been at the heart of the race row between striker Luis Suarez and Manchester United's Patrice Evra during an Anfield match in October, for which Suarez was banned for eight games by the FA.
"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," Liverpool said in a statement on Sunday.
"Liverpool Football Club has been forthright and resolute for many years in its stance against racism and any form of discrimination," the club added on their website.
"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."
A tearful Adeyemi was consoled by Liverpool captain Steven Gerrard after the incident in the second half of the Premier League club's 5-1 win.
"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," added the statement.
