Silva has been rested for the Champions League trip to Russia, while goalkeeper Kepa Arrizabalaga (shoulder) and Marcos Alonso (suspension) are also out.
After drawing 0-0 with Sevilla in their Champions League opener, Frank Lampard's side also recorded a goalless draw with Manchester United at Old Trafford.
New goalkeeper Edouard Mendy and veteran defender Silva have won praise for their roles in helping to solidify a Chelsea team which leaked more goals than any other team to finish in the Premier League top 10 last season.
Zouma praised Silva's impact but thinks Chelsea have shown they can shine even before he was signed on a free transfer from Paris Saint-Germain.
"We have quality everywhere," Zouma told reporters. "Before Thiago we were doing good too. There is nothing to prove. We are here as a team to win the game.
"Everyone has been training hard. Defensively we have done a great job. Communication has been better too and the lads have made an unbelievable effort.
"I don't think we can talk about turning a corner [yet]. We are doing our jobs but that's only two games. We want to keep doing that.
"Thiago brings experience. He has been trying to talk to players, help people - which is great for us. He brings calm."
Antonio Rudiger is in contention to play for the first time this season after holding talks over his future with Lampard, with Andreas Christensen and Fikayo Tomori the other options to partner Zouma at centre-back.
Hakim Ziyech is also in with a chance of making his first start for Chelsea as they eye a first Group E win against an injury-hit Krasnodar side who picked up a point in their first game against Rennes.
Asked about reports he held heart-to-heart talks with Rudiger, who was close to a move away in the transfer window, Chelsea manager Lampard said: "I have had discussions, I saw the story.
"I've always had a positive relationship with him. Sometimes players are out of the squad but he is very much in contention to play.
"We've played high-level opponents in the past two games. I didn't like every bit of it but we are still improving.
"The balance isn't as great as I want it to be. It's something we're working on every day - we want more and it will take work."