The Gunners pushed hard to sign the midfielder before the summer window shut at 11pm BST on Thursday night, making a trio of formal offers, with the last reaching £25million.
However, Villa flatly rejected all three approaches and had no plans to sell Luiz so late in the window.
The Brazilian, who is into the final year of his contract, will now carry on playing for Villa and Gerrard isn’t worried about the impact of the Arsenal saga on his performances.
Asked if he feared about Luiz’s mindset moving forward, the under-pressure Villa boss said: “Knowing the boy and the player, I doubt it.
“I have got confidence he will 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 on 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 face to face yesterday and he understood where it was at, and the position that the club was in.
“He very much respects the decision. Hopefully it’ll calm down in the hours and days coming, and he’ll be fine moving forward.”