The Brazil international was the subject of two unsuccessful bids from the Gunners during the final hours of the summer transfer window.
He said: “I have confidence that he’ll understand the situation and the club’s decision that we didn’t want to lose a very important player and a top player so late in the window.
“From a personal point of view I very much back the club’s decision and stance on that.
“I spoke to Dougie yesterday on that and he understood where it was at and the position that the club was in and very much respects the decision.
“Hopefully it’ll calm down in the hours and days coming and he’ll be fine moving forward.”
With the January transfer window now just over two months away, Arsenal remain keen on Luiz and he is said to be high on the agenda for Gunners manager Mikel Arteta and technical director Edu.
The arrival of Marseille star Boubacar Kamara had threatened Luiz’s place in Gerrard’s first-choice lineup but the French midfielder is now expected to be unavailable until after Christmas after suffering a knee ligament injury.
That could leave Gerrard and Villa with a dilemma ahead of the January window as Luiz remains a key place within their squad - but will also enter the final six months of his current contract over the turn of the year.
That would allow him to negotiate a pre-contract agreement with a club outside of the Premier League with a view to making a free transfer move next summer.