The Brazilian, whose contract expires at the end of the month, returned to action after the three-month hiatus with a forgettable performance. After coming off the bench to replace the injured Pablo Mari in the first half, Luiz made a glaring blunder to gift Raheem Sterling the opening goal of the contest.
He followed that up by hauling down Riyad Mahrez in the second stanza, conceding a penalty and being sent off for good measure.
"It's my fault," the 33-year-old said after the match. "The team did well, especially with 10 men. The coach is amazing, all the players are amazing, it was my fault."
Luiz, who has conceded more penalties and made more errors leading to goals than any other Premier League player this season, added that he was wrong to focus on his contract status in the buildup to the league's return.
"I should have taken a different decision in the last two months but I didn't," he said. "All about my contract, if I stay here or not. I have 14 days to be here and that's it. ... I should have tried to decide my future as early as possible, but I didn't.
"I don't want to use that as an alibi or excuse, it's my fault, and that's it. ... I love to be here. That's why I continue to train hard."
Manager Mikel Arteta refused to pin the blame on the veteran center-back, though, instead commending him for taking responsibility after the match.
"He has spoken in the dressing room," Arteta said, according to the BBC. "David is someone who is very honest.
"My opinion has not changed from the moment I joined the team and it won't change because of a difficult performance tonight."