The arbitration panel had upheld the Premier League's decision to fine West Ham 5.5 million pounds ($11.17 million) for breaking transfer rules in the signing of Tevez and fellow Argentine Javier Mascherano, who has since moved to Liverpool.
Sheffield United, who were relegated, wanted West Ham to be docked points and had sought to overturn their own relegation.
On
Friday the High Court ruled that there had been no error in law with the panel's decision but the Yorkshire club, who are also seeking compensation, have not ruled out other action.
"The application was made on very narrow grounds and has also been denied on very narrow grounds," the club said in a statement on their Web site www.sufc.premiumtv.co.uk.
"Sheffield United has not precluded taking further action, whether against the Premier League or West Ham and we are currently considering our position with our professional advisers."
