Instead of returning the ball to Cardiff keeper David Marshall, Canaries midfielder Fer kicked the ball into an empty net after it was put out of play to allow an injured Norwich player to receive treatment, deep into injury time.
The goal was not allowed to stand, but a melee followed involving several players from both sides, and the fine is for that, rather than Fer's behaviour.
A statement from the FA read: "Norwich City have been fined the standard penalty of £20,000 after admitting a breach of FA Rule E20(a) in relation to their game against Cardiff City on 26 October 2013.
"The charge was that the club failed to ensure its players conducted themselves in an orderly fashion in or around the 94th minute of this fixture."
Cardiff have also been charged with the breach but they have rejected the standard penalty and their fine will now be decided at a separate hearing.