Following a series of controversial calls that went against his side, Ribery took to Instagram to express his frustration with the outcome of the quarter-final second leg.
Arturo Vidal was sent off in the 84th minute for a second yellow card, though replays appeared to show the Chilean's tackle was clean.
Madrid went on to score three times in the additional period – two of which were scored by Cristiano Ronaldo and appeared to be offside – to down the German champions 6-3 on aggregate.
Ribery posted screenshots of two of Ronaldo's goals with a curved line "proving" the Portuguese was, in fact, onside.
Ribery then posted another message saying: "One year of hard work, thank you referee, bravo!"