The German giants were dumped out of the competition on penalties by second-tier side Holstein Kiel and Flick was extremely "disappointed" to taste defeat.
The Bayern boss said: "It’s a shock of course. We’re very disappointed, we wanted to defend the treble.
"Taken altogether, it was down to details, the team showed great spirit. We were dominant, which was our aim. It’s very annoying that we conceded the equalizer in the last second."
Flick also credited Bayern's opponents for pulling off the upset and urged his team to put the result behind them as their hopes of winning successive trebles went up in smoke.
He told the club website: "We must congratulate Kiel, they made it a real cup fight, they were completely committed.
"We must put it behind us and do things better. We must be more compact at the back. We must apply more pressure and be more solid when it comes to balls over the top. It’s surprising, that’s what the cup is like. Kiel defended well, their keeper turned in an outstanding performance. It just happens in penalty shootouts, I don’t blame (Marc) Roca at all."
Bayern forward Thomas Muller added that the Bayern had been left "very disappointed" by the shock result.
He said: "The bottom line is that we lost to an underdog from Kiel, who put everything on the line. It’s very, very disappointing."