Spurs set up the tie after victory at Carlisle United.
Vertonghen told the London Evening Standard: "You would rather play at home in a cup competition but Norwich are a team we can beat. Chelsea and Manchester United are playing each other, Manchester City are out, Everton are out, so a few teams have gone and there are possibilities for us.
"I've had a good start here but adapting quickly was what I hoped for. I'm not 19, where I can wait for two or three years. I'm 25, I want to play well now and so far it's happening. I've got my first goal and that's a good start."