Wednesday night's 6-1 win over Nordsjaelland in their final Group E game proved futile as Juventus won away to Shakhtar Donetsk to consign the Blues to the continent's second-tier competition. But defender Luiz declared there was no point "crying" over what was a moment of unwanted history for the club 200 days after their greatest night.
Luiz said: "The Europa League is glamorous for me. I don't have this title so I want to win it. I look to the Europa League like I did the Champions League because I don't have this medal. We can do great things in this competition."
The Brazil star - who will miss Chelsea's first Europa League match after incurring a ban for his latest yellow card - added: "You have great games in the Europa League. There are great teams in this competition. Chelsea don't have this competition so they need to win this title."
That is exactly what Chelsea did in the Champions League last season in ending their agonising wait to be crowned kings of Europe. Their reign will technically continue until May, but that was scant consolation to the club's red-faced players.
"There was embarrassment in the dressing room and also sadness," Luiz said. "We won the Champions League last season and to get knocked out after the group stage is a great disappointment. This is a big club and big clubs deserve to play in big games. The best games in the world are in the Champions League."
To make matters worse for Chelsea, their alarming slump in the Barclays Premier League has left them in real danger of failing to qualify for next season's competition.
Anything other than a first league win in eight attempts at Sunderland on Saturday and they could arrive in Japan for the Club World Cup outside the top four. Even a victory may not be enough to prevent them surrendering a Champions League spot in their absence, with their rivals all playing another fixture in that time.
Luiz said: "I am sad but football is quick and we have another game in two days and another big competition in one week. I can't spend three or four nights crying - you have to look to the next match. We have a difficult game on Saturday so need to change our mood.
"Chelsea need to play in the Champions League every year and the players have this inside our heads."