Karl-Heinz Rummenigge described Bayern Munich's last-gasp Champions League exit at the hands of Inter Milan as a "dagger through the heart".
Goran Pandev curled home the decisive goal in the 88th minute on Wednesday to give the holders a 3-2 victory at the Allianz Arena and send them through on away goals.
Bayern had been in total control at half-time, leading 3-1 on aggregate, but they missed a host of chances to kill the tie off, failing to take advantage of woeful Inter defending.
Wesley Sneijder pulled one back for the visitors before Pandev completed a sensational comeback and booked the defending champions' place in the quarter-finals.
"That was a dagger through the heart. We were too naive in the second half. The task now is to salvage what can be salvaged in the Bundesliga, and that won't be easy," chairman Rummenigge told the club's website.
Coach Louis van Gaal, who will leave his post at the end of the season, admitted his side were the architects of their own downfall.
"Losing like that is very disappointing," he said.
"Yet again, we've brought it on ourselves, and not for the first time this season. We've learned nothing from our mistakes, and that's a shame. We created so many chances, but we've failed to put them away. We didn't keep it as tight in the second half.
"We've brought this defeat upon ourselves, and that's the most painful thing, because you can't say Inter were better than us. We now have to lead the team out of this trough, because we still have our target of qualifying for next season's Champions League."
Bayern lie in fourth place in the Bundesliga table, two points off the Champions League places.
Van Gaal's players also bemoaned their inability to see out the game.
Mario Gomez, who scored Bayern's opening goal, said: "We have only ourselves to blame. We're gutted, because we were superb for 65 minutes. It really hurts."
Bastian Schweinsteiger added: "It's unbelievable that we've been knocked out by Inter Milan. I'm deeply disappointed. I thought Inter were physically exhausted, they could hardly run any more. But we've still not managed to play it cleverly."
Arjen Robben said: "We're making the same mistakes over and over again. It's unbelievable, we should have been 4-1 up. We've conceded three goals at home again, and that just can't be happening."
