Last season Griffin took the NFL by storm in his rookie season by guiding his side to the playoffs with a 10-6 record, winning the Offensive Rookie of the Year award in the process.
However, after sustaining a knee injury in the playoffs the 24-year-old has found it difficult to reach the heights of the 2012 season, as his team slipped to a 3-8 record following their defeat to the San Francisco 49ers on Monday.
Shanahan told reporters: "[Last year] We had a dual threat. Now that threat is not quite there, as strong as it was a year ago. But now we go to a different direction, with our play action, we still run some of the zone reads, so that will come. That maturity will come, there's a growing period.
"If you take a look at so many of these quarterbacks, all the Hall of Fame quarterbacks, they've had much tougher periods than we've gone through so far. It doesn't happen overnight, but he's got all the ability in the world to make that big jump, and you just have to be patient."
Griffin has thrown 14 touchdowns to 11 interceptions this season, a year after throwing 20 TDs to just five picks.