Manager Carlo Ancelotti branded the spot-kick loss at Parc des Sports - where midfielder Thiago Motta had been sent off during extra-time, before Zlatan Ibrahimovic and Thiago Silva both missed from 12 yards - as a "disaster" after witnessing chances of the domestic double disappear.
Nevertheless, PSG - eliminated from the quarter-finals of the Champions League by Barcelona - remain in the driving seat some nine-points clear of Marseille at the head of Ligue 1 with just six games left.
Victory over Nice at Parc des Princes tomorrow night would press Ancelotti's men ever closer to a first championship in 19 seasons.
Lucas, who hopes to be back in the side following a rib injury, insists there will be nothing other than complete focus against Nice.
He told a news conference: "Obviously, we are very sad (about the cup defeat). We are disappointed because we wanted to win.
"But everybody also wants to win against Paris Saint-Germain, which makes things more difficult.
"Now we must focus on the rest of the season, to win the next matches. "
Lucas feels PSG showed with their run to the last eight of the Champions League that they can also be a force in Europe once again.
"We had two big games against Barcelona. I think we showed talent which was enough to have earned qualification (for the semi-finals)," he added.
"We are proud of what we have shown, and we were eliminated by a huge team.
"This will increase our motivation for the championship tenfold.
"We have shown that we have the opportunity to do some thing in the European Cup next season."
Nice are fifth following last weekend's comfortable 3-0 win over Sochaux, and left them out of the top four only on goal difference.
Coach Claude Puel believes the fight for European qualification will go to the wire.
He said on the club's official website, www.ogcnice.com: "From second to 10th place, all of the teams look to above.
"We will just play our game, and see where it takes us.
"We just wanted to fight, to live out a good end of season."
Nice, though, have been handed a blow with the news 16-year-old sensation Neal Maupay needs surgery after snapping the anterior cruciate ligament in his right knee while playing for the reserves.
"In his misfortune, Neal can fully concentrate on his rehabilitation, and I am sure he will come back even stronger," said Puel.
"We have tried to protect him in terms of his amount of game time and the media pressure. At least now he will be able to prepare for his school exams in peace."