The Russian side exited the competition on Wednesday in what was Semak's final game in charge - despite picking up a 2-1 victory at Signal Iduna Park thanks to goals from Hulk and Rondon.
Despite that, Semak was still pleased with Zenit's endeavour and claimed that the mistakes from their first-leg 4-2 defeat were too difficult to recover from.
"We made too many mistakes [in the first leg], almost all of which led to a goal. We played below our level in that game and this handicap is very difficult to win back," he told reporters.
"We are well aware how difficult it is to win back that deficit created in the first leg and unfortunately Borussia did not allow us to seriously fight back."
Semak also hailed the spirit within the squad and thanked his players, having been at the helm since Luciano Spalletti's departure earlier this month.
"For today's game thank you very much guys - especially those who did not get into the starting line-up because that is always the hardest," he added.
"On the field it was evident that that team is playing as one. They fought and fought and I am sincerely grateful to them all."
Semak will be succeeded by new coach Andre Villas-Boas on Thursday.