Sections of supporters inside Upton Park booed their own players on Wednesday night despite seeing their side beat Hull City 2-1.
Downing has now urged fans to provide a positive atmosphere around the club during the final few weeks of the season.
"You need your fans onside because the biggest thing at a football club is the fans. We've not given them much to shout about during a difficult season, but they've stuck with us the whole way through and I'd ask them to stay with us right to the end," he told West Ham's official website. "If we keep getting results, we'll stay in the Premier League.
"I won't let it affect me as an experienced player, but it can affect the younger ones, so I would ask the fans to stick with the players at home and we'll try to get them results."