Shanahan said he learned of the sanction hours before the start of last year's free agency, forcing him to scramble at the last minute to alter the team's plans.
There's a clear look of anger in his face anytime he mentions the penalty, but he said he can't comment in detail until the matter is completely resolved.
General Manager Bruce Allen last month called the sanctions "wrong" and "unfair" and said the Redskins were still trying to get them overturned.
But there's been no hint from the league that anything will change before the start of free agency on Tuesday at 4 p.m.
Without the penalty, the Redskins would be substantially under the cap, able to not only re-sign their own players but also free to be a competitive bidder on the open market for their positions of need — notably safety, cornerback and right tackle.
With the penalty, the Redskins ended the season over the cap, meaning they would need to cut players and restructure contracts before the Tuesday deadline.
Cornerback DeAngelo Hall and ageless linebacker London Fletcher, who had left ankle surgery Wednesday and then tweeted that he plans to return for a 16th season, are among those whose large 2013 cap numbers could merit some tinkering.
The Redskins made several moves Saturday, agreeing to multiyear deals with tight end Logan Paulsen, fullback Darrel Young and linebacker Rob Jackson. Their expected to wait as long as possible to announce the cuts.
More than anything, the Redskins could use a big-time safety after a season in which they finished 30th in pass defense and allowed 58 completions of 20 yards or more.
A first-round draft pick would normally be an option, but the team gave up its top pick in this year's draft in order to move up last year and take Griffin at No. 2 overall.
The cap penalty makes the search that much tougher. And it also means they might have to find a new special teams captain.
"There are three or four other teams that are definitely going to come after me," Alexander said. "And I'll have to make the decision when it comes. I just hope the Redskins are in the ballpark."
Follow Joseph White on Twitter: http://twitter.com/JGWhiteAP