Only Hull City or Newcastle can be relegated this weekend after Sunderland's 0-0 draw at Arsenal on Wednesday kept them up, and a home win against the Hammers would guarantee the Magpies another season in the Premier League.
But a draw for John Carver's side might not be enough if Hull defeat Manchester United at the KC Stadium as they currently boast a goal difference advantage of seven.
Dummett, however, is adamant he and his team-mates will do their utmost to get the win which will ensure safety.
"It's still in our hands," he said. "I think the fans are probably sick of us saying that as we've let ourselves down in the past where we didn't produce but luckily it's still in our hands now, it doesn't matter what happens with Hull as long as we win our game then we'll be ok.
"The more games that have been coming and the more games we've been losing, the pressure's been building and building and building. Now it's come down to the crucial time where we can no longer make any excuses, we have to produce this Sunday coming.
"I think a lot of players in this squad have never been in this position before so there's a lot of pressure. I think especially me as well being a local player, being a fan, not wanting the club to go down, it's something I don't want to see happen.
"There are a few players who have got experience, who have been relegated before, and they know exactly how it felt and what it was like. They're desperate - everyone in there's desperate for it not to happen again."