After three defeats on the spin there is a real danger the Hammers could be overtaken by bitter rivals Tottenham for a place in the top half of the table.
But left-back McCartney, 26, said: "We are all determined to finish above Spurs.
"We know what it would mean to us and to the fans. If we don't, it will be a major disappointment.
"We are still four points clear and three of our last four games are at home. We have to make them count."