Bundesliga giants Bayern were held 1-1 by their English Premier League opponents at the Allianz Arena.

The German side dominated proceedings in the familiar surrounds of their own stadium, but proved unable to make home advantage count, losing on penalties after Bastian Schweinsteiger missed his spot-kick.

"The team which played better lost and, because of that, the defeat really hurts," goalkeeper Neuer said.

"There's a complete emptiness in all of us. We're very disappointed. We have not talked much in the locker room since the final whistle. Everybody is busy with their own thoughts and all of us are sitting there with heads held in our hands."

Bayern president Ulrich Hoeness was at a loss to explain the result after seeing his team spurn numerous chances in front of goal.

"You know yourself how the game went," he said.

"In the past you talked about such a game (for) months afterwards. Nowadays you just remember the result - Champions League winner 2012: Chelsea FC.

"Nobody can understand how they have done it, Chelsea probably cannot understand themselves, but that is football."

The loss means Bayern have now gone consecutive seasons without lifting silverware for the first since 2009, but club  captain Philpp Lahm is adamant the team still has more to give.

"We're bitter about the result," he said.

"We wanted to win the Champions League, but we just fell short.

"If you want to take any positives from the defeat, then it's the fact that our team is currently in the best shape that it's been in for a long time.

"We're going to play for the next years with the same group of players and after this defeat we're more hungry for trophies. Nevertheless it has been a very disappointing evening for us."