The Ukrainian champions are currently playing home matches in Lviv - more than 700 miles from their Donbass Arena stadium - due to political unrest in the east of the country.
Shakhtar qualified from Group H, along with Porto, but were dealt a tough tie with 2013 champions Bayern, and Lucescu says his side could have done with a bit more luck when it came to Monday's draw.
"At this stage of the Champions League, I did not want Real Madrid, as they are the current holders of the trophy, I did not want Barcelona, because we have already played with them many times, and I did not want Bayern," he said.
"Today, Shakhtar are in a difficult situation: without our stadium, without our fans, playing constantly on the road.
"Bayern are one of the strongest teams in Europe, who have incredible support and attract packed stadiums.
"I repeat: I did not want them precisely at this stage.
"Naturally, Bayern are favourites in this duel. But in football anything is possible."
The first leg will take place at Arena Lviv on February 17.
