The hosts kept Jurgen Klopp’s men at bay for the vast majority of the game, and could have taken the lead when Alexander Tettey’s effort hit the post after the break.
Liverpool got the breakthrough when substitute Sadio Mane, who was making a return from injury, brought Jordan Henderson's long ball under control in the penalty area, before blasting past Tim Krul.
The Canaries are now winless in their last three Premier League matches and currently sit bottom of the league with just 18 points out of 26 games.
After the game, Farke said they played against the best team in the world but insists he was disappointed with the result.
"It’s disappointing because we played very well, but it was a moment of magic from [Sadio] Mane that proved crucial to Liverpool winning this game,” the German coach said.
"When we create chances we have to be effective, when you are two-on-one on the goalkeeper it must be a goal but sadly we missed that chance.”
"We were playing the best team in the world. It was sad that during a period that we had more control that they were able to score. We were close to a good result but have to accept the loss.”
"When you watch our last 15 games or so, barring one game, they have all been decided by one goal."
Next up for Norwich City is a visit to the Molineux Stadium to face Wolverhampton Wanderers.
