Blues have achieved some notable results against the leading sides this season, most notably a home win over champions Chelsea.
But centre-back Davies knows they have to get the best of their closest rivals to ensure their top-flight status for next season.
He said: "You'd say that we need four more wins but I think the most important thing is to beat the teams around you."
He added: "We lost to West Brom a couple of weeks ago and it catapulted them up the league and kept us down there.
"If you beat the teams around you, it gives you a bit of breathing space because at the moment, a lot of them are getting good results.
"West Ham have improved from a position where people were saying they are already going down, so it is a tough ask.
"It is so tight that one win can catapult you up four or five places and hopefully on Saturday we can get that win at Wigan.
"Wigan is a massive game. Our form if anything has been better away from home.
"I don't know if that is because of the shape we play. To get three points there would be massive in helping us to stay up."