Los Rojiblancos need to win and for Qarabag to at least avoid defeat at Roma at the same time for Diego Simeone's men to avoid a premature exit and fall into the Europa League.
Costa forced through a return to Atletico after three seasons at Stamford Bridge featuring 59 goals in 120 appearances, plus two Premier League titles, but is ineligible until January due to their transfer embargo and has remained in Madrid to work on his fitness.
"Diego is a huge player. He scores a lot of goals and important goals," Luis said. "It is frustrating seeing him playing like an animal, but he can't play. It's just a month until he can play with us. He'll help us a lot. He came back to Atletico because Chelsea couldn't keep him because it's his desire. He really wanted to come back to Atletico.
"He knows the club, he knows the way we play. He has already adapted. I know it was difficult times for him and for Chelsea. Now everybody's happy. We want to see him play and happy again."
Simeone and Luis insist Atletico's sole focus will be on beating Chelsea in Champions League Group C.
"We don't have to be looking about what happens in Rome," Simeone said. "We just have to think about us. It's not going to be a simple game. We need to take the game to where we feel we can hurt them. It's a personal challenge to fight for everything we've worked for these last few years and keep our values there."
Left-back Luis, who returned to Atletico after a single season at Chelsea in 2014-15, said: "It depends all on us. We need to win and then we'll have to wait. We can't do anything else. If we don't manage to qualify, we will have to concentrate on what comes, on the next competition, and try to win those games."
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies