They are tears of anger, sadness and the result of his first visit to Ukraine since Russia invaded his homeland over a year ago.
Zinchenko returned a few weeks back, visiting a school in Chernihiv Oblast (a province in the north of the country) that had been hit during a missile attack.
Where once there were classrooms, there now is rubble. Just 10 per cent of the school is still standing.
“It’s a completely different story when you see these destroyed buildings by your own eyes rather than your phone,” says Zinchenko, speaking back in London.
“Imagine trying to sleep through the night with your babies, with your kids, and then suddenly there is a siren from 1am to 5am.
“You need to wake up, go underground to the bunker and hide yourself. You never know where the bomb or rocket might hit.”
As well as the missile attack, the school was in an area that was occupied by Russian troops for 33 days last year. The children’s stories explain Zinchenko’s tears.
“Imagine you are a kid and you see someone coming with a mask on in your house to steal, but this is even worse,” he says.
“The guys are coming with guns, they do much, much more scary things and then they just leave.
“These were real true stories from the kids. It was honestly… I was like in shock. You cannot see it even from movies. Kids cannot lie, they are just talking the real truth.”
Zinchenko has been helping his country ever since war broke out, the Arsenal defender immediately thinking: “How can I help? What can I do? What can we send?”
Zinchenko and Shevchenko met during their recent trip and the trio have united for Game4Ukraine, a charity match at Stamford Bridge on August 5.
All of the funds raised by the match will help rebuild the Mykhailo-Kotsiubynsky Lyceum school in Chernihiv Oblast.
Zinchenko knows the real heroes are on the frontline but he is doing all he can.
“For me, it’s impossible to compare,” he says. “I can help from here, much more to my country and to the people, rather than if I would be there at the moment.
“But, I promise, that I really want to be there – even now – because last week when I just arrived there… I don’t know, this is my homeland. I just went in, and I just want to be there. That’s it, that’s it.”
Zinchenko hopes that under Zelensky a better Ukraine can be built, but right now the stories he tells paint a bleak picture.
“One scary story, I heard about one woman, holding two little babies, born just a few months ago,” he says having spoken to volunteers at the destroyed dam in Nova Kakhovka.
“She was on the roof with two of them, holding the last stone and trying to survive. Unfortunately, she didn’t, with the kids.
“Listening to these stories — real stories, not from the internet — you just think… for what? To achieve what?
“I am angry every single day because I really want to know what they are doing – to achieve what? To win what?”
Hearing Zinchenko speak, it is incredible to think he has just competed – and excelled – in an Arsenal team that pushed Manchester City all the way in the Premier League title race.
How did he cope when his homeland is at war?
“Oh please, please don’t get me in my head because I don’t know what is there at the moment,” he says. “Honestly, it’s incredible.”
Football has helped. Being on the pitch is the one place Zinchenko can forget, even if only for 90 minutes.
“That’s why I think today football is such a powerful opportunity to stick together, to be united, to send any messages you want, to have fun,” he says. “Since the invasion my head was lost, but still me and my family were talking a lot about this, and we have to keep going.
“Football is my life and when I am on the pitch, I am starting to forget about everything.”
Zinchenko also seen first-hand the power of football. On his trip to Chernihiv Oblast, he and Shevchenko had a kickabout with the children caught up in the war. For a brief moment, smile and laughter returned to the playground.
“Our heroes they are losing their lives, they are taking the risk of their lives on the frontline,” he says. “So that’s why we have to keep going, otherwise…I know guys everyone has some fatigue, I know, but in my case I cannot stop.”
Zelensky is not stopping either and, as much as Zinchenko’s trip to Ukraine left him sad, it also inspired him to keep working for a better future.
“The things he (Zelensky) does are incredible,” says Zinchenko. “Watching all this process from the inside, the people around him, how they work is unbelievable.
“They don’t stop. They. Don’t. Stop. It looked like they weren’t tired at all. I believe with this kind of energy, with these kind of people, we have a bright future.”
Zinchenko truly believes that is possible and plans to live in Ukraine when he one day retires. He has one child with his wife, Vlada, and they are expecting another.
“I just want to do something good,” he says. “So when they grow up, they will ask me: ‘Daddy when this war was in our country what did you do – how much did you help people?’
“I just want to look at my babies’ eyes and I just want to say: ‘Me and your mum, we were trying to do our best’. That is what is in my head.
“You have two options: to give up or the other way is try to help as much as you can. I am so proud of my people and to be Ukrainian.”
Game4Ukraine is taking place at Stamford Bridge on August 5. Tickets are on sale now at game4ukraine.com. Game4Ukraine will be broadcast live in the UK on Sky and free to stream for those in Ukraine