Bayern s Thomas Mueller reacts after receiving another goal during the German Soccer Cup match between Borussia Moenchengladbach and Bayern Munich at the Borussia Park in Moenchengladbach, Germany, Wednesday, Oct. 27, 2021. Borussia defeated Bayern with 5-0. AP
"We were picked apart from A to Z in the first half," the 32-year-old Mueller, who made his Bayern debut in 2008 and is approaching 600 appearances for the Bavarian giants, told ARD.
"I don't know if I've ever experienced anything like that before in an FC Bayern shirt. We have to apologise to our fans."
A full-strength Bayern team was pole-axed Wednesday when Gladbach took the lead at Borussia Park with barely a minute gone.
After Kouadio Kone's early goal, Algerian defender Ramy Bensebaini netted twice to make it 3-0 at half-time.
Bayern's bright start to the second-half was obliterated when Swiss striker Breel Embolo scored two rapid-fire goals.
Furious Bayern sports director Hasan Salihamidzic described the visitors' performance as "a collective blackout -- we simply didn't turn up".
Gladbach fans started celebrating long before the final whistle as the song 'Oh, wie ist das schoen' (Oh, how beautiful this is) echoed around the stands.
"Of course, this was a disgrace for us," added Mueller who said the Bayern team sat stunned in the dressing room afterwards.
"We had a lot planned. We tried to somehow pick ourselves up, but I don't think you saw that on TV."
Bayern had plenty of off-field distractions in the build-up.
Head coach Julian Nagelsmann was sidelined at home, isolating after testing positive for Covid-19.
Defender Lucas Hernandez discovered the morning of the second-round cup tie that he will escape jail in Spain despite violating a restraining order in 2017.
Midfielder Joshua Kimmich has been heavily criticised in the German media after opting against being vaccinated for Covid-19.
Nevertheless, those factors do little to explain a dreadful team performance as Bayern suffered their heaviest cup defeat in club history.
A backlash is expected away on Saturday in the Bundesliga when Bayern play at Union Berlin, who are unbeaten in their last 21 home league games.
"People are used to us showing a reaction after negative experiences. But that's easy to say," said Mueller.
"Normally, we are also used to reacting differently after falling behind."
Nagelsmann's assistant coach Dino Toppmoeller promised improvement.
"We will certainly have to live with gloating and ridicule in the next day or two. That's the business," he said.
"But we have to brush ourselves off and show a reaction on Saturday. That will come -- for sure."