Kyle Shanahan is penalized Sunday. (John McDonnell/The Washington Post)

The NFL has fined Washington Redskins offensive coordinator Kyle Shanahan $25,000 for Sunday’s incident in which he berated a replacement official, according to observers, during and after a loss to the Cincinnati Bengals, a person familiar with the league’s decision said Tuesday.

Shanahan was upset, he said in a written statement Monday, that an official told Redskins Coach Mike Shanahan late in the game that a false start penalty would result in a 10-second runoff and end the game.

There was no 10-second runoff, but Kyle Shanahan’s reaction cost the Redskins a 15-yard unsportsmanlike conduct penalty.

The officials erroneously marked off 25 yards instead of 20 yards in penalties, and the Redskins threw an incompletion on the final play of their 38-31 defeat.

Television cameras caught Shanahan following the replacement officials off the field, and observers said he profanely criticized one of them.

The Redskins declined to comment Tuesday evening through a spokesman. It was not clear Tuesday night if Kyle Shanahan had been notified about the fine.

When asked Monday about the possibility of Kyle Shanahan, his son, being fined by the league, Mike Shanahan said: “I think we’ll let the powers that be take a look at what transpired on both sides and let them make the decision.”

The penalty comes after NFL teams were warned recently that coaches should treat the replacement officials respectfully.

Kyle Shanahan has not been made available to reporters to speak about the incident. The Redskins declined interview requests Sunday and Monday. He is scheduled to have his weekly meeting with the media Thursday.

In his written statement Monday, Kyle Shanahan said he conducted himself “in the wrong way” and his emotions “got the best” of him.

“When I overheard the official tell the head coach that the game was over after the false start penalty, I tried to explain that the game was not over,” Shanahan said. “That is what resulted in the unsportsmanlike conduct penalty. I tried to get an explanation of how I could get that penalty when half of the other team was on the field as well.

“I was frustrated, and in the process of trying to get some answers from the officials, I conducted myself in the wrong way.”

The Redskins were called for a false start as they lined up for a play from the Cincinnati 34-yard line, just after rookie quarterback Robert Griffin III spiked the ball to stop the clock with seven seconds remaining.

After the unsportsmanlike conduct penalty was assessed, the 20 yards in penalties should have resulted in the ball being placed at the Redskins 46-yard line. Instead, the officials placed the ball at the Redskins 41. Griffin’s Hail Mary pass toward the opposite end zone on the final play fell about 10 yards shy of the goal line and was incomplete.

“I ask our players to hold themselves to a high standard and be accountable and I know that I’m accountable for my actions as well,” Shanahan said in Monday’s written statement.

“I know that I need to handle those situations better in the future. My emotions got the best of me and I know it’s my responsibility. This will never happen again.”

When asked if he was disappointed in Kyle Shanahan’s handling of the situation Sunday, Mike Shanahan said Monday: “He thought the game was over and I think he shared that with you. I’m not going to go into a lot of detail on it. But I tried to explain to you that the official told me that the game was over. We knew the game shouldn’t be over. They had half their football team on the field. What I was trying to do was get a personal foul, talking to the official because he had told me the game was over. I said the game was not over and I think we should have a 15-yard penalty [on the Bengals]. But that wasn’t the difference in winning and losing the game. Those things do occur. You would like cooler heads would prevail. That’s what I expect.”