Doubts over boss Chris Hughton's future crept in after the Canaries won just once prior to Sunday's 1-0 victory at Stoke.
But Snodgrass, 26, said: "We're in the Premier League and there's pressure. I'll be honest, too, and say that if you can't handle that pressure, then there's no point in being here.
"In your job, every day, you put pressure on yourself. The manager puts that pressure on us and the fans put the pressure on the players and the manager - it's not just the manager, we're all in it together.
"He's spent maybe £27m on players and the manager will tell you himself that there is an added pressure when you have a bigger kitty to spend."
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