The Bavarians cancelled out their 2-1 quarter-final first leg defeat to take the game to extra time in
But they had Arturo Vidal sent off with a controversial second booking, eventually losing 4-2 – 6-3 on aggregate – to miss out on the biggest club prize in Europe and have goalkeeper Manuel Neuer ruled out for eight weeks with a broken foot.
Two of Cristiano Ronaldo’s three goals were clearly offside, adding to Bayern’s frustration and anger with the referee’s decisions after being eliminated by a Spanish team for the fourth consecutive time in the competition.
One of Bayern’s goals should also have been ruled as offside.
“We were hung out to dry, that’s what happened,” Rummenigge told a post-match dinner in the early hours of Wednesday. “I am furious, so furious tonight as I have never been.
“The team was literally in ruins in the changing room,” he said. “Anyone wanting to blame the team tonight must have watched a different film.”
Bayern may be out of
They will have to do it, though, without Neuer, who broke his foot in the game, according to Rummenigge.
Neuer, outstanding in both legs against Real, was injured in extra time and will miss the final stretch of the season, with Bayern leading by eight points in the Bundesliga with five matches remaining.
They also host rivals Borussia Dortmund in the German Cup last four next week.
With only one win from their last three league matches, Bayern know only victory will do against lowly Mainz 05 on Saturday to tighten their grip on a record-extending fifth straight league title and avoid seeing second-placed RB Leipzig close in even further.
Bayern’s lead has shrunk to eight from 13 points only a few weeks ago, and coach Carlo Ancelotti will now need to assess how central defenders Jerome Boateng and Mats Hummels held up after having to play without having fully recovered from their injuries.
“The adductor muscles at some point in the second half just clamped shut,” Boateng said. “I tried to just battle through, but it was not easy.”