The Gunners sealed their place in the quarter-finals after goals from Sokratis and Eddie Nketiah helped them secure a 2-0 win at Fratton Park.
"It's important to continue doing the job that we're doing every single day," Luiz told BT Sport after collecting the man of the match award.
"We're improving a lot but have to be humble. We understand we are not there yet.
"In the last game, we did amazing but then we lose. That's football, and we have to understand why we lost. Tonight, I'm so pleased with the team.
"The young boys are improving a lot every single week, they have a great mentality. They understand what high level is and know you have to bounce back. They have to be ready to react and understand our football."
On debutant Pablo Mari, Luiz added: "He's great. Everybody was 100 per cent focused, I'm so pleased we didn't concede.
"Pablo is a great guy, great player, he had an amazing game. We are here to help each other and we have 25 players ready to play for Arsenal, ready to do the job. [When it's] like that, it's a pleasure to play football.
"I will say to the guys, especially the young lads, that they are starting their football careers and have a great opportunity to play for a big club."