The Hammers take on Manchester United at Upton Park on Saturday and Downing believes that a victory will allow the players to look up, rather than worry about the threat of relegation.
"We're not out of the water yet and we need points as quickly as we can, starting against Manchester United. If we play to our strengths I think we can beat them," the England international insisted on the club's official website.
"I think that realistically tenth place is a good place for us to aim for. We know that a couple of wins can get us there and above the teams around us, and I believe we have one hell of a chance to get there."
West Ham are currently 12th, six points clear of the relegation zone and just three points behind Aston Villa, who occupy 10th spot.