Shanahan put Grossman into the game with 1:50 left and Washington trailing by six points. The backup quarterback fumbled on his first play and Ndamukong Suh returned it to seal the Detroit Lions' 37-25 victory.
"I felt with the time and no timeouts, he was the best chance to win in that scenario," Shanahan explained. "Just knowing the terminology of what we've done, how we run it."
McNabb refused to publicly question the eyebrow-raising choice.
"He makes the decisions, I just continue to go with it and just cheer for my team," he said. "We had opportunities we just didn't take advantage."
Cornerback DeAngelo Hall said Monday it was "definitely a shocker" that McNabb was pulled. He said it raises the question: "After the season, will he be here or not?"
The Redskins (4-4), who have a bye this week, will have a lot of time to work on correcting their mistakes and likely answer McNabb-related questions.
The six-time Pro Bowl quarterback has his lowest rating since 1999 when Philadelphia drafted him No. 2 overall and he started six games.
Shanahan said McNabb is still the team's starting QB. If that is still true in two weeks after a bye, McNabb will get another chance against his former team when the Redskins host the Eagles in a Monday night game.
Washington had a 25-20 lead with 4:40 left when Alphonso Smith stepped in front of McNabb's pass at the Redskins 41 to set up the go-ahead TD.
"My arm got hit, so I wasn't able to follow through with the throw," said McNabb, who was 17 of 30 for 210 yards with a TD and an interception.
McNabb was benched for just the second time in his career. The other time was two years ago against Baltimore, when he was playing for Philadelphia.
"You just have to learn from it and move on," McNabb said. "I did it then, and I'll do it now."
Information from The Associated Press was used in this report.