The Potters have drawn their last three games to edge up to three points from safety ahead of the day's 3pm kickoffs with two games left to play.
Although the three teams above Stoke in the table - Swansea City, Huddersfield Town and West Ham United - all have a game in hand on Paul Lambert's side, Chelsea loanee Zouma remains optimistic of beating relegation.
"The game plan was to try and win, we knew they would press us and attack," Zouma told Sky Sports News.
"We were solid at the back, the effort from every single player was great, we deserved the draw. The target was to grab something from here and we did.
"There are two games to go, we need to win those. It is not going to be easy but with the mentality and effort we showed today we can keep going. There is a big belief we can stay up, everyone is confident."
Stoke are now without a win in 12 Premier League games, their longest run without a victory in the top flight since December 1984.