The Hammers will face Manchester City for a place in the quarter-finals.
Asked about playing on his 27th birthday, Zouma added: "It's a big day for the team. Hopefully we can go through and win the game, as that's the most important thing."
On West Ham's recent run of form, Zouma added: "That's the mentality of the team. Everyone wants to fight for his place and his spot and everyone is doing well at the minute. We're training very hard and the manager gave us the mentality to never give up and that's what we do.
"We're playing the great, we're having the ball and we don't concede, so it was a great win with three wins and three clean sheets. We want to continue like that but it's going to be difficult so we have to stay focused."
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