"Obviously there's going to be some roadblocks for every quarterback in the league, and obviously he's going through a tough situation right now," Shanahan said on "The Waddle & Silvy Show" on ESPN 1000. "But my opinion is he'll work through it, and Chicago will be very proud that they have him as their quarterback."
Cutler played under Shanahan with the Denver Broncos from 2006 to 2008 before being traded to the Bears last year. Cutler struggled in Chicago, throwing 26 interceptions to go along with 27 touchdowns as the Bears stumbled to a 7-9 record.
"I don't care what quarterback you have, you have to have a good supporting cast," Shanahan said. "And not only a good supporting cast, you have to have a system that really relates to the players.
"That's what you're working for as a head coach in the National Football League, to put all of that together."
Shanahan, a self-described Cutler fan, had nothing but positives in describing the 26-year-old quarterback.
"[He's a] Pro Bowl player; had a good supporting cast around him [in Denver]," Shanahan said. "A worker; very smart; handles himself like you want. I thought he was just getting better and better."
Shanahan didn't subscribe to the theory that Cutler can be too cocky.
"I like the way he handles himself," he said. "I like the way he competes. I like him on a day-in, day-out basis. I think people will see his personality in time, and hopefully it's a short time [until he has] a little success."
The Redskins recently signed former Bears and Houston Texans quarterback Rex Grossman to a one-year deal. Shanahan believes Grossman will adjust to the system run by his son, Kyle Shanahan, who was the Texans' offensive coordinator last year.
"I think Rex feels very comfortable with the system," Shanahan said. "He thinks it's a system he enjoys and can take full advantage of his skills.
"I haven't had a chance to spend any time with him on the field, but I got a chance to know Rex through the years, and hopefully he'll come in there and compete and give us some depth. Once a guy gets an opportunity, now he just has to show us what he can do on the field and we're going to give him an opportunity to compete."