Bayern had scored 16 goals during the group stage of the competition and warmed up for the last 16 clash in Lviv with an 8-0 hammering of Hamburg in the Bundesliga.
However, a well-organised Shakhtar side restricted the five-time Champions League winners throughout the 90 minutes, with Andriy Pyatov only tested on a handful occasions.
Lucescu was pleased at having stopped Pep Guardiola's side, but rued not making their man advantage count after Xabi Alonso had been sent off.
"Our first target was not to lose," he said. "And the second target was to give ourselves a chance in the return.
"We have that chance.
"What I regret is that we didn’t try and play our football after Bayern went a man down."
Shakhtar will now aim to repeat the process in the Allianz Arena on March 11 when they travel to Germany for the second leg.
