Sheffield United's bid to regain their Premiership status appears to be over after their bid to see West Ham docked points was dismissed.
Tevez was at the centre of the Sheffield United-West Ham saga
An arbitration panel upheld the Premier League's decision not to dock the Hammers points over the signings of Carlos Tevez and Javier Mascherano.
Sheffield United launched an appeal after they went down on the last day of the season and West Ham stayed up.
West Ham had earlier been fined £5.5m for their handling of the duo's deals.
A statement on Sheffield United's website said: "We are obviously very disappointed by this conclusion.
"In particular, in circumstances where the tribunal recognised that the outcome of the decision turned out to be 'unfortunate in the extreme', and that Sheffield United have done nothing wrong to merit this outcome."
The Hammers were found guilty on 27 April of acting improperly and withholding vital documentation over the duo's ownership.
When Tevez and Mascherano were registered as players, West Ham failed to disclose that they had entered into an agreement with third-party companies.
The Blades had wanted the panel to order a new disciplinary commission to deal with the London club.
Sheffield United also lost another claim - made jointly with Fulham - that the Premier League should have forced West Ham to de-register Tevez.
The tribunal had sympathy for Sheffield United's grievances ... but it was impossible to find that the decision to fine West Ham was irrational or perverse."
Ruling from arbitration panel
A statement from the arbitration panel read: "The tribunal have found in favour of the FA Premier League on both issues and dismissed the claims of Sheffield United FC and Fulham FC."
The three-man panel, headed by retired High Court judge Sir Philip Otton, did not have the power to change West Ham's punishment but could have ordered a new independent commission to judge the case.
The ruling from the arbitration panel said Sheffield United would not normally have been allowed to dispute another club's punishment but that there were "exceptional circumstances" because of their relegation, which affected their membership of the Premier League.
The tribunal said they had "sympathy" with the Blades, while West Ham had been "deliberately deceitful" and yet remained in the Premier League.
But they said they could not rule that the independent commission's decision had been wrong to fine West Ham in the first place.
The panel's ruling stated: "The tribunal had much sympathy for Sheffield United's grievances.
"However, the tribunal had to apply the principles of judicial review and determine whether the decision was irrational or perverse.
"This is a very strict test and is very difficult to satisfy.
"It concluded that it was impossible for this tribunal to find that the decision was irrational or perverse."
The performances of Tevez in particular helped the Hammers string together an excellent run of results late in the season which moved them clear of the relegation zone.
Mascherano made less of an impact and moved to Liverpool during the January transfer window.
I would like to reiterate that Carlos Tevez is a registered West Ham United player
West Ham chairman Eggert Magnusson
West Ham were still in danger of losing their Premiership status on the final day of the Premier League season depending on results, but Wigan's win at Sheffield United ensured it was the Blades who were condemned to relegation.
"We are happy that this matter is finally closed and all parties can now move on," said Hammers chairman Eggert Magnusson.
"The arbitration panel's decision is very clear and reflects what we have believed all along.
"West Ham United have been preparing for next season in the Premier League since the final whistle at Old Trafford in May and we will continue to do so.
"I would like to reiterate that Carlos Tevez is a registered West Ham United player with a playing contract that still has three years remaining on it, and that situation remains unchanged."
The decision of Sheffield United's appeal makes it all but certain that the Blades will be playing in the Championship next season.
In relation to Sheffield United's and Fulham's claim that the Premier League should have immediately terminated Tevez's registration, the tribunal ruled they had acted reasonably in allowing the Argentina striker to play in the last three games of the season.
A Premier League statement added: "The panel confirmed that throughout this complex and unprecedented case the Premier League followed the process laid out in our rules and behaved reasonably at all times.
"The panel also understood that this was a difficult situation, exacerbated by the fact that decisions were being made against the backdrop of the climax to the 2006-07 season."