Well, it was not the hardest thing to see coming, Beşiktaş blew up under the pressure of not knowing what to do. To be honest, tactically Beşiktaş were always the same, but the second leg against Club Brugge was also a mental breakdown for both the team and fans. Club Brugge actually showed us there was still hope for Beşiktaş, when they positioned their defense too deep and generously wasted a lot of counter-attacks. Nevertheless, Beşiktaş were unable to dominate the game. This is what creates the difference between a dangerous team and a mediocre team. If you can play a dominant and fluent game when you have enough time and space, then you are a dangerous team, but Beşiktaş was a great example of a mediocre team that is unable to push its limits and organize a system to facilitate creativity.
However, we must reveal the deception behind Slaven Bilic's decision to play with two strikers. First of all, putting more players in a position does not necessarily mean that you are going to be more effective in that position. Thus, Mustafa Pektemek's presence in the Club Brugge's penalty box did not pose any threat to the opponent. In contrast, his existence motivated Beşiktaş's wing players to make more crosses into the penalty box, which mostly finished in the hands of the Brugge goalkeeper. Furthermore, Bilic took one player from the midfield in order to put Pektemek forward and this led to a less resolute midfield to confront Brugge's dangerous counter-attacks. Added to that, it is always easier for the defensive players to control the opponent's forward players in the same area. Therefore, Beşiktaş intensified Brugge's defense in the middle rather than stretching it and making it more vulnerable to penetration.
Slaven Bilic made an emotional decision and deceived himself with the good result against Kayseri Erciyesspor. He could have spent his whole week thinking about how to use the available space and time against Brugge, but it seems that he chose the lazy way of attacking and tried the least creative way to open up the Brugge defense.
On the other hand, the only thing I can say about the mental breakdown of both players and fans, is "pathological." The Arabesque music that comes from Beşiktaş is just rooted too deep and whenever Beşiktaş try to push their limits, they just explode. Despite the awful strategy and game plan, Beşiktaş only needed one goal after the horrible mistake by Tolga Zengin, but the atmosphere in the stadium was crazy. Beşiktaş always have this kind of anxiety given their game play, but fans destroyed what was left on the pitch. Of course, Slaven Bilic and his players are responsible for this humiliating loss, but I have to admit that the fans contributed to the situation a lot.
However, the situation could have been much more different. Bilic could have let Tolgay Arslan to organize the attack rather than Gökhan Töre. Furthermore, seeing as Beşiktaş had no intention to play in a collective manner, at least Bilic should not have changed the formation so drastically. The absence of Atiba Hutchinson also made an undeniable impact, especially on the side's defensive balance. I do not know whether he was ready or not, but Bilic needed him very much. Brugge were not the toughest nut to crack for sure, but Beşiktaş never had the nutcracker. Finally, judgment day came for Slaven Bilic.
I do not know what actually happened to Tolga Zengin, but it seems that it was something mental. He was always anxious throughout the game and could not handle the pressure. There is no explanation for his mistake in the first goal actually. He must have lost control of his body because of anxiety. Any experienced goalkeeper would run for that kind of a long ball. Added to that, he did not give confidence to his team-mates and that made Beşiktaş's defense more vulnerable. On the other hand, Brugge goalkeeper Mathew Ryan put in a brilliant performance and his aerial command made every Beşiktaş cross ineffective. Unlike Tolga, he was very confident and this not only motivated his team-mates but also discouraged Beşiktaş strikers.