Shanahan surprised many by starting Grossman after maintaining throughout the week that John Beck would start against the Miami Dolphins. Grossman threw two interceptions as the Redskins' offense struggled in a 20-9 loss.
"Rex is going to be our quarterback," Shanahan said. "When you go with a veteran quarterback, it's pretty easy -- because usually that situation stays pretty much status quo. Unless there's an injury during the week, Rex would be the quarterback. But crazy things could happen. He could go down during the week."
Shanahan said he was "impressed" by the Way Grossman played.
"Everybody says, 'Well, you only had nine points,' but nine points obviously goes to a collective group," Shanahan said. "But I thought Rex played well."
Grossman began the year as the Redskins' starter but was pulled for Beck after five starts. Beck did not win any of his three starts, and the Redskins offense averaged just 10.3 points per game. Shanahan said Becks' performance speaks for itself.
"I like John's talent," Shanahan said. "I like what we have in John, but I'm always going to do what I think is in the best interest of the team to win."
NOTES: The Redskins offense lost another asset, with the team placing wide receiver Leonard Hankerson on injured reserve Monday. The rookie receiver tore his labrum in the fourth quarter of Sunday's game after catching eight passes for 106 yards. He was the first Redskins wide receiver to have more than 100 receiving yards in a game this season. ... Backup defensive lineman Kedric Golston tore two knee ligaments on Sunday. Shanahan said the team believes Golston has a third-degree MCL tear and a partial ACL tear and will miss one game at least ... Shanahan said wide receiver Santana Moss, who has missed three games with a broken left hand, will sit out at least one more week but could possibly return for the Nov. 27 game against Seattle. ... right tackle Jammal Brown, who missed Sunday's loss with a groin injury, is a "long shot" to play in the upcoming game.
The Associated Press contributed to this report