The Baggies currently sit 17th on the standings, equal on 25 points with third-bottom Cardiff City, but Mulumbu believes the squad is more than capable of avoiding dropping down to the Championship.
Albion have won just one game in their past 18 outings but hard-nosed midfielder Mulumbu is certain they can break that below-par run and record some vital victories in their remaining ten fixtures.
"We didn't really expect this situation when we started this season. We need to adapt," he told Express & Star.
"We know how hard it is to stay in the Premier League and we'll keep working together as a team.
"We've got some good players, good lads and I'm really confident in my team that we can stay up.
"At the moment there is a lack of confidence and the best thing is to encourage.
"We won't give up because that would be unfair to all the people at West Brom and the fans. We're going to fight to stay in the Premier League.
"I think we need to win four or five games to stay up. To win at Swansea (on Saturday) will be hard - but not impossible.
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