"Within the confines of our collective bargaining agreement, we are trying to have a voice and a hearing in terms of our cap situation," Cowboys director of player personnel Stephen Jones said Sunday.
Jones said the Cowboys hoped to avoid filing any legal action over the cap penalty.
The Cowboys were penalized $10 million against the salary cap by the league because they, along with the Redskins, were penalized for $36 million, front-loaded contracts during the uncapped 2010 season. The penalties were split evenly over the 2012 and 2013 seasons for the two teams.
The NFL Players' Association agreed to have the 2012 salary cap set at $120.6 million rather than a lower number and for the Redskins and Cowboys to take those reductions. Otherwise, the cap would have been significantly lower.
The owners of the other 30 NFL teams will be briefed on the grievance at the owners meetings. Arbitrator Stephen Burbank will rule on the grievance.
ProFootballTalk.com and SI.com had earlier reported on the filing of the grievance.
The Cowboys and Redskins took cap hits during the 2010 season that normally would have been spread out over the length of the contracts giving them an unfair competitive advantage.
"I thought the penalties imposed were proper," John Mara, the New York Giants' owner and chair of the NFL Management Council, which imposed the penalties said Sunday. "What they did was in violation of the spirit of the salary cap. They attempted to take advantage of a one-year loophole, and quite frankly, I think they're lucky they didn't lose draft picks."
Said Jones Sunday: "That's John's opinion. That's not my opinion."
Mara said the Redskins and Cowboys shouldn't be surprised by the penalties that were imposed.
"They attempted to take advantage of it knowing full well there would be consequences."
When reached for comment on the filing of a grievance, the Redskins said they were referring all calls to the league office.
Twenty-eight NFL teams will receive $1.6 million of additional cap space because of the penalties given to the Redskins and Cowboys, sources told ESPN NFL Insider Adam Schefter. The teams receiving money can also choose to split it over the 2012 and '13 seasons however they see fit.
Cincinnati, Denver, Jacksonville, Minnesota and Tampa Bay chose not to take the additional room in 2012, a source said, and will instead get the money in 2013.
Despite the cap penalties, Jones said the issues wouldn't effect the Cowboys.
"Obviously, getting the cap hit, you have to deal with it and there's ramifications of that," Jones said last week. "But it's not going to stop us from being able to do the things we have to do to be a championship-caliber football team in 2012."
In the early stages of free agency the Cowboys signed cornerback Brandon Carr to a five-year $50.1 million contract and two offensive linemen, Nate Livings and Mackenzy Bernadeau to contracts totaling $30 million. The Cowboys also signed quarteback Kyle Orton to a three-year $10.5 million deal to back up starter Tony Romo.
Before free agency started, the Cowboys cleared nearly $17 million in salary-cap space by restructuring the contracts of cornerback Orlando Scandrick, tackle Doug Free and wide receiver Dez Bryant. They also released cornerback Terence Newman and kicker David Buehler.
Last week the Cowboys cleared an additional $1.55 million in cap space by releasing veteran guard Kyle Kosier.
Information from ESPN.com NFC East blogger Dan Graziano, ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.