Luiz, whose contract with the club runs out at the end of the month, came on as a 24th minute substitute for the injured Pablo Mari but endured a dreadful night.
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The central defender was at fault for Raheem Sterling's opener just before the interval and then gave away the penalty for the second goal four minutes after the restart.
"It's my fault," he said, "The team did well, especially with 10 men. The coach is amazing, all the players are amazing, it was my fault."
Luiz suggested he should have resolved his contractual situation by now but said his status was not a factor in his performance.
"I should have taken a different decision in the last two months but I didn't," he told Sky Sports.
"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 -- that's it. I love to be here. That's why I continue to train hard."
Gunners manager Mikel Arteta said Luiz had held his hand up after the game and suggested his display wouldn't impact on any decision about his future.
"I don't know what will happen with his contract. I know what happened today, I know the way David reacted, as a player and as a person as well, he can handle the situation," he said.