Shanahan, who worked under his father Mike Shanahan, said that he learned a lot about his role working with RG III and is hoping to take that experience into his new role.
"Robert and I had two years together," Shanahan told the Washington Post. "We did a lot of real good things together. I'm very proud of that first year.
"I think he arguably had one of the best years in NFL history for a rookie quarterback. I enjoyed coaching him. It challenged me, because I had to do some things that I hadn't done before, so I had to look at tape in a different way and try to put some different things in.
"I think that improved myself. I'm able to see the game a little differently. I was able to do some things with Robert that I hadn't been able to do with other quarterbacks, and that was really fun to do."
Shanahan was appointed to his new role on Monday.