Spurs lost 1-0 to Wigan on Sunday and are five league games without a win.
King said: “We have to improve, otherwise we will go down. It is simple.
“We need people to stand up and fight for each other and be counted as men and as players.
“That has not been happening enough, which is why we find ourselves in this position.
“We are not playing well away from home but when that happens, you have to work hard and maintain your focus.
“We are conceding late goals because of a lack of concentration.
“We are switching off and that sums us up at the moment.”