The Bayern defense performed poorly under Klinsmann. He implemented a 3-back line that gave up 5 (!) goals in the home opener. He eventually had to revert to the traditional German 4-back line and double stoppers that his predecessor used and thereby lost authority/credibility with his own system..
He was replaced about 2/3's of the way into the season after being embarassed by Barcelona in the CL and it became too risky a gamble on reaching a Champions League spot in the Bundesliga..
Bayern is a very traditional club. Not the best fit for Klinsmann who brought in all new coaches (who didn't speak German) and training techniques. He also changed things such as their traditional pre-game hotel, and publicly demeaned players.
Bayern is run by former world cup players.They're very professional and give their coaches a lot of leeway. The coach has to produce, though. Not reaching the CL is not an option for Bayern.
But Klinsi did wonders for Die Mannschaft in the World Cup, they greatly overachieved there, I think his ideas better translate to the international game.