The 29-year-old scored Spurs' winner over Southampton and now has the Canaries in his sights as the teams duel for a place in the quarter-finals of the competition
Fourth-placed Spurs beat the Saints with Dempsey scoring the winner in a dominant 45 minutes from Andre Villas-Boas' men, but Dempsey believes it will be tough at Carrow Road.
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"It's going to be a difficult game," the American told the club's official website.
"I saw the game against [Aston] Villa. It was at Villa Park and they were taking it to them in the second half so Norwich are a team that does have quality and a good work rate.
"We will have to go there, be sharp and put in a professional performance, but I feel that if we go there and play as we are capable of and perform as we did in the first half at Southampton, we will be fine."
The game sees Canaries boss Chris Hughton face his former side, where he spent 24 years during spells as both a player and a coach.