Shanahan said Wednesday at the NFL Annual Meeting that he learned of the league's official sanction, which was issued for dumping large base salaries in an uncapped 2010 season, an hour before the start of the free-agency period, according to The Washington Times.
Citing the ongoing arbitration case to dispute the penalties, Shanahan declined to comment further.
The Dallas Cowboys also were docked $10 million in cap space and have joined the Redskins in formally protesting the punishment. On Tuesday, NFL owners voted to uphold the penalties against the two teams.
Shanahan also defended the Redskins' decision to trade three first-round draft picks to the St. Louis Rams to acquire the No. 2 selection in the 2012 NFL Draft. The Redskins will have the opportunity to draft either Stanford quarterback Andrew Luck or Baylor quarterback Robert Griffin III, and Shanahan said acquiring a franchise signal-caller is a necessary step to making the team competitive.
"The Super Bowls that I've been involved with, with Steve Young, with John Elway, both were franchise quarterbacks," Shanahan said, according to ESPN.com. "They can make plays when everything breaks down. And if somebody can do that, then you've got an opportunity, once you get to the playoffs, to do something special.
"Now, can you still win without one? Sure you can. But you'd better be pretty special."
Shanahan doesn't know whether it will be Luck or Griffin who falls to him -- Indianapolis Colts owner Jim Irsay said Monday his team hasn't decided what it will do with the No. 1 pick -- but the coach said the Redskins would be happy with either quarterback.
"That's a decision, when you get to the second pick, you've got to feel great about both guys," Shanahan said. "There can't be any, 'Oh, I hope I get this guy, I hope I get that guy,' because you don't know what's going to happen. You know what's reported, but you just don't know, especially with this process. But when we did move up to that position, we had to feel great about both of them before we gave up what we gave up."