The Baggies' 2-0 defeat to Fulham last Sunday means Tony Mowbray's side remain at the foot of the table after going four league outings without success.
With just 12 league matches left, 2008 summer signing Zuiverloon believes they must look to get something out of their daunting-looking trip to Everton this weekend.
"We need to start winning. It doesn't matter how," he told the club's official website. "We just need the points.
Away form"We need to try to win all our home games and some away games too. We feel we can cause an upset at Everton.
"We have enough quality to win some games against teams people wouldn't expect us to beat.
"We have to focus on away points too - but it needs belief from everyone."
Zuiverloon added: "We know Sunday's performance was not acceptable. We lost to a better team.
"But if you don't believe you shouldn't be playing football. We still have a chance and we know we can do it (escape relegation)."