The Brazilian scored a penalty as the Blues hammered Nordsjaelland 6-1 in their final Group E game - a victory that proved irrelevant as Juventus secured a 1-0 win at Shakhtar Donetsk.
That left Rafa Benitez's side the ignominy of becoming the first reigning European champions to exit at the group stage, but although Luiz admits a degree of embarrassment, he is quickly refocusing on the Europa League.
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.
"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.
"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."