Tom Hicks and George Gillett, the owners of the club, sought to block a 300 million pound ($476 million) sale to New England Sports Ventures, saying the bid was too low.
Royal Bank of Scotland brought the complaint to court, saying that the board changes violated the club's contract with the bank, Bloomberg News reported.
Liverpool Football Club is England's most successful soccer team, and has been champions of England 18 times. It has not won the domestic title in 20 years, and has seen star players such as Spain's Xavi Alonso defect to other clubs.
Meanwhile, fans have grown to loathe Americans Hicks and Gillett, blaming them for the club's stagnation in recent years.
Justice Christopher Floyd denied Hicks and Gillett an appeal. Still, they can go to a higher court.