The Tigers boss was also warned as to his future conduct following his post-match opinions, which the governing body felt breached FA rules.
The FA have confirmed on their official website that Bruce admitted the charge which 'called into question the integrity of the match referee, and/or implied that the match referee was motivated by bias, and/or brought the game into disrepute'.
The Premier League clash at White Hart Lane was decided by a controversial 80th-minute penalty which was scored by Roberto Soldado.
The Spain striker netted the only goal of the game after referee Michael Oliver had penalised Hull's Ahmed Elmohamady for handball.
The Egypt international was in close proximity to Jan Vertonghen as he went to cross the ball, but the match official pointed to the spot.
Bruce described the penalty award by Oliver as "a joke decision" adding: "I have to ask the question, would we have got it? In my opinion, he couldn't wait to give it."