After succumbing to a 2-0 defeat at Manchester City on Wednesday night, the Hammers stay in 18th position, one point adrift of safety.
However, despite their winless streak in the top flight being extended to five matches, Snodgrass feels that the first-team squad contains the right players to ensure that the club do not drop down to the Championship.
The Scot told talkSPORT: "We've got the players to do so. I think the Brighton game (which ended 3-3), everyone will be disappointed with because we were in a great position and a few mistakes slipped, that's when you let teams back in.
"In the Premier League if we are going to stay up we have to stop letting teams back into the game. Be ruthless and go and finish teams off, that's what we're working on."
West Ham are next in action when they face Liverpool at Anfield on Monday night. body check tags ::