The 14th-placed Hammers currently have 31 points with eight games left to play.
Allardyce is confident that seven points between now and the end of the campaign will keep his players in the top flight.
"Thirty-eight we'll need and we'll try to get more than that as quickly as we can," he told the club's official website. "I think 38 points will be needed this year."
West Ham continue their fight for survival on Wednesday when Hull City make the trip to Upton Park.