The Ukrainians looked to be heading for the top of UEFA Champions League Group H after forging 2-0 ahead with just five minutes left in Lviv.
However, Porto, who had a Yacine Brahimi first-half penalty saved by Andriy Pyatov, staged a stunning late fightback.
They were given a lifeline in the final minute when Yaroslav Rakitskiy was penalised for handball in the box and substitute Jackson Martinez tucked in the resulting spot-kick, before the same player stole in at the near post to finish Cristian Tello's low cross in the 93rd minute.
Lucescu was understandably downbeat after the game, which was played 760 miles away from his side's Donbass Arena because of the unrest in eastern Ukraine.
"I don't want to talk too much," said the Shakhtar coach, whose team have two points from two Champions League games and travel to BATE next.
"We were so happy before the end of the match - we were euphoric - and then we conceded two goals. We are very upset now. There's nothing more I can say."
