Alex Teixeira and Fernandinho gave Shakhtar a 2-0 lead and although Oscar pulled one back with two minutes to go, the defending champions could not force the equaliser.
It means Shakhtar have deservedly taken charge of Champions League Group E in the first of what could be a crucial double-header.
Luiz was at a loss to explain Chelsea's display tonight and told Sky Sports 4: "I don't know.
"They don't give you the opportunity to win the game.
"We did not play well - I am shocked by the performance.
"Congratulations to Shakhtar. Maybe now we think just of the next game."