A DeAngelo Hall interception gave the Redskins a 21-7 lead at the start of the third quarter, but the Broncos then scored 38 unanswered points, including four final-quarter touchdowns, to seal a 45-21 victory.
The match was Shanahan's first return to Denver since ending his 13-year spell in charge of the Broncos in 2008, and he admitted that he was especially fired up to face his former team.
"You can't give Peyton [Manning] that many opportunities because he's going to take advantage of it," Shanahan told the Associated Press.
"It's very easy to get kind of fired up, especially coming back here and wanting to win the football game. That's why it's disappointing when you have the opportunity there in the third quarter and you don't take advantage of those opportunities."
The result leaves the Redskins third in the NFC East with a 2-5 record.