The tight end led the team in receptions against the San Francisco 49ers last night, taking five catches for 49 yards.
The 23-year-old told the team's website: "I still get nervous on the field. I'm not as comfortable as I should be. But I'm getting better. I get nervous in a butterflies kind of way. I get a little bit of anxiety before each game.
"I'm trying to do my best and I want to do my best to help this team. I'm trying to impress [teammate Antonio] Gates. I'm trying to impress the coaches. I'm trying to show what I can do."
Head coach Mike McCoy added: "He's a talented young player that's got some potential for us. He's got a great guy to learn from. Seeing the way he runs routes, he talks to him a lot of times and you see the communication. He got off to a good start tonight which is great to see."
Green has recorded 161 receiving yards and scored two touchdowns during the pre-season.