Having repeatedly declined to answer questions about his future as head coach, Shanahan walked out of the interview room after being asked if he was doing anything to quash the media scrutiny.
"I'm not going to talk about that," Shanahan replied when initially asked about his job status following the Redskins' 27-26 loss to the Falcons in Atlanta after missing a two-point try with 18 seconds left.
"I'll talk about football and about the (Dallas) Cowboys and the (New York) Giants," he said of the Redskins' remaining opponents for the season.
Shanahan has one year and $7 million left on his contract and reportedly has no desire to step down, despite a woeful 3-11 campaign by Washington who sit stone-last in the 16-team National Football Conference.
Last week, Shanahan had announced he would bench starting quarterback Robert Griffin III for the last three games of the regular season, using instead back-up Kirk Cousins.
On Sunday, with Griffin watching from the sidelines, Cousins led a fourth-quarter scoring drive to pull his team within one point of Atlanta before Shanahan elected to go for a winning two-point conversion instead of a tying extra point.
However, the pass from Cousins was deflected by Desmond Trufant and the Falcons (4-10) held on to edge the Redskins after scoring 20 points off seven Washington turnovers.
"I've never been involved with a team that had seven turnovers and had a chance to win it," Shanahan told reporters. "So I'm very pleased with the effort.
"You can't win with turnovers, yet we still had an opportunity to win and that shows you how hard they fought. Those guys normally are great with ball security and don't turn it over."
Shanahan, who led the Denver Broncos to Super Bowl victories in 1997 and 1998, is also vice-president of football operations with the Redskins, giving him control over player personnel with the team.