Heung-Min Son scored a 79th minute winner after Teemu Pukki had cancelled out Dele Alli's first half opener from the penalty spot.
Norwich require a miracle to stay up
The defeat on Wednesday left Norwich six points adrift of Premier League safety with just 14 matches to play this season.
"We know it will be a big sensation - maybe a miracle - that we stay in this league," Farke told his press conference after the game (via BBC Sport).
"We have to be realistic. When you get promoted into the best league in the world, you have to handle the expectations a little bit. We have had the biggest injury crisis of all our competitors at this level as well. We have not had a lot of luck."
The Canaries have picked up just five points from their previous six matches in the league and face Burnley at Turf Moor in the FA Cup fourth round on Saturday.
Relegation battle a good experience
While battling relegation would not have been Farke's goal at the start of the season, the German said it was proving a good experience for his players.
"A relegation battle is good to experience," he said.
"It shows the character and personality of the players. We were praised a lot last season for that and we've shown it again this season. You learn the most out of a not-so perfect game. We were self-critical and this experience will help us at Tottenham."
Norwich finished top of the Championship last season with 94 points from 46 games, 11 points clear of third-placed Leeds United.
However, City have managed just four wins in the Premier League this season, winning just once on the road.