The Europa League offers last season's Champions League winners an opportunity for a semblance of redemption in Europe after their humiliating exit from the top tier competition at the group stages.
Speaking ahead of Thursday night's last 16 first leg encounter with Steaua Bucharest, Luiz said: "This is a great opportunity to win another European title. Last season it was in the Champions League, everybody was happy.
"I have the hunger again and I think Chelsea have the hunger again to win titles.
"This is one big club. This is the way you need to think to play for a big club.
"[Tonight] it's an opportunity to win one more game, the first leg and we're looking for the title of the Europa League."
With Manchester United out of the Champions League, Arsenal's European campaign likely to be completed next week and Newcastle and Tottenham in challenging last 16 ties, Chelsea could again fly the flag in Europe this term.
Brazil international Luiz added: "It's important to show the Premier League is the best league in the world. Chelsea and other teams have the opportunity to show that.
"Last season we did a great job. This season we have another opportunity, in another competition, but it's still here."
Luiz is greedy for success in a week in which Chelsea's chances of silverware this term could improve, or come to an end.
The FA Cup holders tackle Manchester United, the runaway Barclays Premier League leaders, at Old Trafford in Sunday's quarter-final, with Luiz targeting two victories in four days.
"We need to be focused from the first minute until the last minute [tonight] and Sunday's a big game," Luiz said.
"All the world want to watch this game and Chelsea go to Manchester to win."
Luiz believes it is imperative the players continue to be honest with each other after reports emerged concerning dressing room unrest.
With a permanent managerial appointment on hold until the end of the season and Rafael Benitez in interim charge only until May, leadership often appears to be coming from the players.
"This is the key for big clubs to win titles and win games," said Luiz, who insists he is happy to play in defence or midfield.
"In Chelsea we have a strong team, strong changing room. All the players play together.
"It's difficult sometimes when we've lost games. People speak a lot.
"But I think in Chelsea we have a great family, great players and the players to support this pressure.
"I've now been at Chelsea for two years. In bad moments and in good moments I take my responsibility to help the young players, like the other two Brazilians [Oscar and Ramires].
"I love that. I love pressure, I love responsibility."