"What annoys me most is that we lost the game even though our opponents played with 10 men," said Buruk.
Juventus had initially taken the lead through a penalty from Manuel Locatelli (30th minute). Shortly after the break, however, Italy's record champions suffered a major setback, as defender Lloyd Kelly was sent off with a red card, putting Galatasaray in a strong position.
Nevertheless, Federico Gatti (70') and former Schalke player Weston McKennie (82') sent the visitors into extra time with their goals.
"I was annoyed and surprised on the sidelines," analysed Buruk. "Our players' performance was really weak."
'Important evening to recognise weaknesses'
Goals from Victor Osimhen (105+2) and Baris Alper Yilmaz (119) enabled Gala to progress, but the team from Istanbul will need greater consistency in the future if they are to remain in the competition.
After the 5-2 victory in the first leg, they believed Galatasaray could "make it to the final", said Buruk
The 52-year-old sees his team's poor performance as an opportunity to make changes.
"For me as a coach, it was a good evening to improve my team. It was important to recognise our weaknesses. I'll discuss that with the players and it will help us in the round of 16."
There, the Lions from Istanbul will face either Liverpool or Tottenham Hotspur. Their next opponents will be decided on Friday at the draw at the UEFA headquarters in Nyon.