The Hammers have lost their last two fixtures but a run of four wins before that means Sam Allardyce's side remain six points clear of the relegation zone.
A tough run-in sees West Ham face Liverpool, Arsenal, Tottenham and Manchester City before the end of the campaign, with reigning champions Manchester United visiting Upton Park on Saturday.
But England winger Downing believes there is enough quality in the squad to keep the east London club in the top flight.
"We're confident we can get out of it," he 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."
Andy Carroll was recalled to the starting line-up in the weekend defeat at Stoke for the first time since returning from suspension.
The club-record signing opened the scoring in that 3-1 defeat and Downing is pleased to have his compatriot back in the side.
"Andy did really well," he added.
"His hold-up play was really good because he was getting kicked about a bit from the centre halves, but he got his goal.
"That will be good for the confidence with nine games to go, so for him he just needs to carry on and play like he did on Saturday. He's a real asset for us."