The Canaries are in the top flight after back-to-back promotions and Barnett says that the Norfolk club can look no further than trying to avoid dropping straight back to the Championship as they continue to prepare for life amongst the country's top clubs.
"As far as I know the aim is just to stay up, and establish ourselves as a Premier League team," said Barnett.
"If it's fourth-bottom then we will have done our job, we want to stay out of the bottom three.
"I'd take fourth from bottom. I want to stay in the Premier League and play there next year and the year after.