The fines come as the league and its referees' union were meeting amid reports they were close to ending the lockout of the regular officials.
Belichick grabbed an official's arm at the end of Sunday night's game after the Ravens kicked a winning field goal. Shanahan was cited by the league for "abuse of officials" in Washington's loss to Cincinnati.
"It was inappropriate for me to contact the official. I take responsibility for what happened," Belichick said in statement released by the team. " I accept the discipline and I apologize for the incident Sunday night in Baltimore." Shanahan, the son of Redskins coach Mike Shanahan, was called for unsportsmanlike conduct for berating officials in the final seconds of the Redskins' 38-31 loss. He also confronted an official in a stadium tunnel after the game.
"Any time you do what he did you're going to get fined, and that's the nature of the game," Mike Shanahan said. "If you don't abide by the rules, you're going to pay a penalty and usually after a guy pays 25 grand, they usually learn very quickly." Also, the NFL said Baltimore Ravens coach John Harbaugh won't be fined for making contact with a game official during Sunday's 31-30 win over New England. Ray Anderson, the NFL's vice president of football operations, said Harbaugh did not violate the rule regarding abuse of officials.