The 21-year-old made a permanent switch to the City Ground from the Gunners yesterday in a deal worth a reported £1m.
"It is a team game, so I will work hard to get a starting place," the Nottingham Post quotes Lansbury as saying. "I have to make an impression in training to earn the start.
"I have to impress, because I am at a new club. It is good to get a fresh start and play week in, week out somewhere. It is a great bunch of lads here.
"But I know I need to work hard in training and get used to the squad. I have played against a few of the lads before. Now I am looking forward to playing with them."
Lansbury was in attendance last night to watch Forest's 4-1 defeat to Wigan Athletic in the second round of the league cup.