Allardyce is now eager for his side to put their recent woes behind them and start picking up wins.
"I'm not nervous about the league position," he told the club's official website.
"I'm concerned that history tells you it's not the position that matters, it's the points total you have against games you've played and at present our points total is less than the games played. It's very dangerous.
"We can't keep saying we're playing well but not getting results. Everyone at this club is being paid to win and we're not winning the games we should be winning. We've got to get back to winning ways as quickly as we can."
West Ham's next match in the Premier League is at home to London rivals Chelsea on November 23.