The Ukrainian club were rank outsiders to win the second leg of the last-16 encounter at the Allianz Arena, and their odds further drifted when Kucher fouled Mario Gotze in the penalty area - earning the hosts a penalty, and seeing the Ukrainian outfit lose a man.
After the first leg in Ukraine ended scoreless, a score draw or a win in Munich for the visitors would have seen them advance to the last eight - but the early penalty, converted by Thomas Muller, was a setback.
It was the beginning of a 7-0 onslaught - eliminating Shakhtar, who have been battling with their ongoing displacement.
Shakhtar have been based out of Lviv since July, due to political unrest in the east of Ukraine.
Lucescu said Kucher's red card was a significant setback, before they finished with nine men due to a late injury to Darijo Srna - the Croatian unable to be replaced with the Romanian coach already using his three changes.
"Congratulations to Bayern. We weren't able to carry out our game plan after the early red card," Lucescu said, as reported by UEFA.com.
"We lost in all aspects of the match. They were mentally stronger too. When Srna went off, the game was finally over for us.
"We played with just 10 men. We lost this game, there is not so much to say about it. But I feel sad that we lost with such a result."
