An arbitrator Tuesday dismissed the challenge by the Washington Redskins and Dallas Cowboys to salary cap cuts imposed by the league in March.

Arbitrator Stephen Burbank ruled that the NFL and its players union had properly amended their collective bargaining agreement and the two teams could not challenge the decision.

The Redskins lost $36 million in salary cap space over two years for the way in which they structured some players’ contracts during the 2010 season, when the NFL had no salary cap. The Cowboys suffered a $10 million salary cap cut over two years. The NFL concluded that the two teams’ actions were an attempt to gain an unfair competitive advantage in subsequent years when the salary cap was reimposed.

The Redskins and Cowboys issued a joint written statement in which they said they would abide by the ruling, seemingly bringing the matter to a close.

“We pursued our salary cap claim pursuant to the CBA and we respect and will abide by the arbitrator’s decision to dismiss,” the teams said in their statement. “We will continue to focus on our football teams and the 2012 season.”

The NFL had asked Burbank, a University of Pennsylvania law professor who is the sport’s system arbitrator, to dismiss the case because the league and the NFL Players Association agreed to the salary cap reductions. That left the teams unable to bring such a case before Burbank, the league contended.

The teams had denied wrongdoing and had pointed out that the contracts were approved by the league at the time.

The NFL Players Association had no immediate comment.

Burbank, in a 10-page decision, wrote that a March 11 “reallocation” letter from the league and players’ union to the two teams informing them of the salary cap reductions, along with a March 27 vote by almost all NFL teams to affirm them, represented a proper amending of the sport’s collective bargaining agreement.

The objections by the Redskins and Cowboys “all must fail as a matter of law if the reallocation letter, as originally executed or as ratified by the March 27 resolution, constitutes a valid amendment of the CBA,” Burbank wrote.

Later in the decision, he added: “The CBA and valid amendments thereto are binding on the clubs.”

One legal expert said Burbank’s ruling was based solely on a rejection of the Redskins’ and Cowboys’ contention that they were entitled to bring such a case to arbitration under the collective bargaining agreement.

“He dismissed it without getting to the merits of the Cowboys’ and Redskins’ claims about whether the salary cap penalties represented collusion,” said Gabriel Feldman, director of the sports law program at Tulane University. “He didn’t get at all into the commissioner’s ability to protect the competitive balance of the league. It was based solely on the owners reaching an agreement on the cap penalties and the union agreeing to them.”

“Professor Burbank found that all clubs are subject to the CBA, and you don’t get to pick and choose which parts you do and don’t like,” Feldman said.

The teams voted, 29-2, at their annual league meeting in March to affirm the salary cap reductions after they had been imposed. The Redskins and Cowboys voted against the resolution and the Tampa Bay Buccaneers abstained.

The league found that the Redskins and Cowboys technically violated no salary cap rules but attempted to gain an unfair competitive advantage, people familiar with the case have said. According to those people, the teams reworked contracts to pay money to players during the uncapped year that otherwise would have been paid in later seasons, when the salary cap was back in effect. That way, the teams cleared cap space for those subsequent seasons.

The 2010 season was played without a salary cap under a provision in the previous labor agreement between the league and union. The cap went back into effect last year with the completion of a new 10-year labor deal.

A person familiar with the union’s view of the case previously said the NFLPA believed the Redskins and Cowboys did nothing wrong but agreed to the cap reductions to avoid the cap being set lower for all 32 teams.

When the union agreed to the reductions, the $46 million in cap cuts was redistributed to 28 of the other 30 NFL teams and the salary cap was set at $120.6 million per team for this season.

It’s not clear how much the salary cap reduction affected the Redskins’ offseason maneuvering. The arbitration proceedings were supposed to be confidential, and Redskins officials have refused to comment in detail, before the arbitration case was filed and after it was put before Burbank.

During the annual league meeting in March, Redskins Coach Mike Shanahan said: “I’d like to talk about that and when I can, I will. But we’re not allowed to talk about it. Believe me, I’d like to. But I can’t.”

Shanahan hinted that day that the salary cap reduction had affected the Redskins’ offseason moves. He mentioned the team’s salary cap situation in answers to reporters’ questions about quarterback Peyton Manning and linebacker London Fletcher, without elaborating on the impact. The Redskins met with Manning when he was a free agent; Manning signed with the Denver Broncos.

But it’s not clear whether the Redskins would have had a better chance of signing Manning without the penalty, and the Redskins were able to re-sign Fletcher. They also made a series of other moves in free agency, including the signings of wide receivers Pierre Garcon and Josh Morgan on the day the market opened.

Redskins officials will have much more time to plan for next year’s reduced salary cap than they did this year. News of the cut emerged on the day before the free agent market opened.

According to several people familiar with the case, some owners initially urged NFL Commissioner Roger Goodell to strip draft picks from the Redskins. The league imposed the salary cap reductions instead, requiring that each team absorb at least half its cap cut this season.

People familiar with the case said the May 10 hearing before Burbank focused on the league’s request to have the case dismissed. If Burbank had allowed the case to continue, another hearing might have been required for other issues to be addressed.