Pep Guardiola admits fatigue ended Bayern Munich's hopes of winning the treble after losing their German Cup semi-final by missing all four penalty kicks in a shoot-out with Borussia Dortmund.

Just two days after being crowned German league champions for the 25th time, Bayern were knocked out of the domestic cup as Tuesday's semi-final finished 1-1 after extra-time before Dortmund claimed a 2-0 victory on penalties.

The defeat came at an extra cost as striker Robert Lewandowski is doubtful for next Wednesday's Champions League semi-final at Barcelona after suffering a fractured cheekbone and concussion, while Arjen Robben is out for the season with a torn left calf.

The shoot-out at Munich's Allianz Arena got off to a dramatic start when Philipp Lahm and Xabi Alonso both slipped to fire Bayern's first two penalties over the bar.

Mario Goetze then had his effort saved by Dortmund goalkeeper Mitchell Langerak while taking Bayern's third penalty before Manuel Neuer hit the cross bar with the fourth spot-kick to send Dortmund to the Berlin final on May 30.

Bayern's coach insisted he is as proud of his team "as never before", but admitted their punishing current schedule of a game every three or four days had taken a heavy toll.

"That was our best game against Dortmund in the period I have been in Germany, but we were a bit tired in the penalty shoot-out," said Guardiola, who is in his second season with Bayern.

"My team gave it everything and I must congratulate Dortmund, I wish them well for the final."

This was the first time Bayern have lost on penalties since the 2012 Champions League final defeat at home to Chelsea.

"The shoot-out got off to a stupid start, it summed up our game," said goalkeeper Neuer, who had a superb game despite failing to convert Bayern's fourth penalty.

"We could have decided it over 90 minutes. It's a bitter defeat."

Lahm said Bayern only had themselves to blame and should have wrapped up the win in normal time after Lewandowski's first-half goal was cancelled out by Dortmund's Pierre-Emerick Aubameyang late in the second half.

"We missed the chance to decide the game in normal time and in extra-time. The winner in the shoot-out goes to the team with the most luck and it's a shame we won't be in the final, we know what a nice occasion that is."