Shanahan said that opposing defenses will all try to stop Griffin in a different way, but that his being able to play on the ground will make other sides think twice about how to tackle him.
"I think everybody will approach Robert differently, but you've got to get ready for a quarterback that has the ability to run and pass," he told the club's official website.
"There's no question about that. I think everybody could see that he made a couple of plays with his legs, so he is able to make plays where you couldn't really see that in the first four games.
"So, yeah, I think anytime you have a quarterback that can do a few things, it puts a lot more pressure on the defense."
Griffin has thrown 1,448 yards and six touchdowns so far this season.