The Greeks won the first leg 3-1 and Piturca said his players committed too many defensive blunders, describing their Balkan opponents' third goal as "something that happens in a school playground".
"At this level, it's very difficult to recover if you make such gifts," Piturca told a news conference on Monday.
"We were not at the desired level both physically and mentally and we have to do much better.
"We're well-prepared and we have nothing to lose, given the circumstances, and I hope we can succeed."
Piturca said first-choice keeper Ciprian Tatarusanu, who missed the first leg due to back injury, was fit to play but he has yet to decide if he will start the game at the National Arena.
The 57-year-old, however, will have captain Vlad Chiriches, who missed the match in Athens after suffering a broken nose, back in his starting lineup.
"I feel OK, I trained very well and I'm not afraid," said Chiriches who will play wearing a face mask.
"It was disappointing to lose the match in Piraeus (Athens) but now we have to overcome the emotions as I know we can qualify.
"It'll be very difficult if we concede a goal, so we must be careful. They were very strong at set pieces and I hope we'll fix our problems."
Greece coach Fernando Santos again sounded a note of caution ahead of the game in Bucharest.
"It will be a different match," the 59-year-old Portuguese said. "We have an advantage but we know the Romanians have the ability to recover two goals.
"We must protect our advantage but that doesn't mean we will defend during the whole game. We want to play a better match than in Piraeus and to qualify.
"Romania will play offensively but I don't want to allow them to control the match. We want to control it and if we score a goal, this will be a huge relief for us."
The Romanian players practised penalties during training on Monday but Santos said he does not expect the playoff to be decided by a shootout.
(Reporting by Angel Krasimirov, editing by Ed Osmond)
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