Tau was influential in the first half and looked to have set up Nigerian striker Emmanuel Dennis for the opener with a brilliant back-heel into the path of the forward, who found the back of the net.
But the Bafana Bafana striker had strayed narrowly offside as he received the ball and the Video Assistant Referee ruled out the strike.
Tau was withdrawn on the hour-mark with the score at 1-1, and Bruges went on to lose as Real’s class shone through.
But the European adventure is far from over for the Belgian side, their third place in the group means they will play in the UEFA Europa League knockout stages.
Brugge will be unseeded in the round of 32, meaning they could come up against the likes of Manchester United, Inter Milan, Ajax Amsterdam, Roma, Arsenal or Sevilla.
The draw for the next stage will be held on Monday, with the two legs to be played in February 2020.