The Royals are seven points adrift of safety in 19th place in the table as they prepare for Saturday's testing trip to Arsenal.
They also have away games against Norwich, Fulham and West Ham to come, while Southampton, Liverpool, QPR and Manchester City have still to visit the Madejski Stadium.
Zingarevich told the Reading Post: "We have a chance. We're in the Premier League and there are eight games to go, eight winnable games.
"It's a tall order, but if you look back a couple of games, we had a good chance of staying up. It changes.
"I think that we probably need to win five out of the eight, but what is most important is the next game and trying to win that.
"We've shown this season we can win games by being more solid - we have beaten good teams both at home and away. This team can definitely win games, we just need to pull together and try to get over the line."