Sam Allardyce's men looked to be heading comfortably for safety after winning all four Premier League matches in February, but this month has started with two consecutive losses.
That has left the London club just six points above 18th-placed Sunderland, who have two games in hand.
The 3-1 reverse to Stoke City on Saturday was a timely reminder of West Ham's vulnerability, but Downing is confident they have what it takes to stay up.
"We're confident we can get out of it," Downing told the club's official website. "The four wins in a row during February proves we can get results, but we've lost our last two and we have to correct that.
"We've got Manchester United next which will be a big test for us and we need to get points on the board."
West Ham host United on Saturday before two matches against fellow bottom-half sides in Hull City and Sunderland.
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