The Canaries secured back-to-back promotions in 2010 and 2011 to return to the top flight.
Snodgrass, who joined the Carrow Road side in the summer, told the Norwich Evening News: "There is a great work ethic and a great belief around the place. There is no big time Charlies or players that get carried away with themselves.
"This club is built on the success from League One and the Championship and when we played against them they were always a hard-working team.
"The boys have got a point to prove. They're all young, hungry lads and we have to keep building on it."
Norwich currently sit 15th in the Premier League table.