Luiz, 33, came off the bench during Arsenal's 3-0 defeat at Manchester City on Wednesday as the Premier League returned to action following the coronavirus lockdown.
His evening ended in disarray, however, as he made a mistake for Raheem Sterling's opener before being sent off just 25 minutes after his introduction for bringing down Riyad Mahrez – with Kevin De Bruyne tucking away the resulting penalty.
Luiz fronted up after the game and took full responsibility for the result, with Arteta revealing he did not start the Brazil international due to his ongoing contract situation.
The former Chelsea defender moved across London last summer but the club only have until Tuesday to extend his one-year deal and keep him at the Emirates Stadium.
Arteta admitted the tighter purse-strings at Arsenal, coupled with the uncertainty over the financial ramifications of the coronavirus crisis, means they must be careful with big-money judgements.
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"We cannot forget the financial situation," he was quoted as saying by Press Association. "The way that Covid-19 has hit every club and the economy in general, it's going to have an impact.
"What the club is doing at the moment is assessing the situation and trying to clarify a lot of uncertainties that we have in the future.
"We have to make big decisions and time-wise it is difficult to fit them in with our needs. We are trying our best and the club is trying their best.
"It is difficult sometimes because it puts the player or our sporting necessities in a difficult situation. Again, we have to adapt. It is what it is.
"That is why I wanted to protect David yesterday. That is why I did not start him. But it's a funny game and after 20 minutes you need him, a player who has had a lot of uncertainty in the last few weeks.
"Don't forget that we have accepted a pay cut, not only the players and the staff, to try to help the situation. I think it was an incredible gesture of unity and commitment from everybody working at the football club that I am very proud of."