Mulumbu remains confident that The Hawthorns outfit can survive the drop, despite a winless run in all competitions that stretches nine matches.
West Brom sit 17th in the table and have won just four league matches this season, but the combative midfielder is positive under-pressure head coach Pepe Mel can steer them to safety.
"I think we need to win four or five games to stay up," Mulumbu told the Birmingham Mail.
"We didn't really expect this situation when we started this season. And we need to adapt to it.
"We won't give up because that would be unfair to all the people at West Brom and the fans. We are going to fight to stay in the Premier League.
"We know how hard it is to stay in the Premier League and we'll keep working together as a team.
"We have got some good players and good lads and I'm really confident in my team that we can stay up."
Mulumbu admitted the squad needed a boost in confidence and called on the club's supporters to back them to the hilt.
"At the moment there is a lack of confidence and, in that situation, the best thing is to do is encourage," he added.
"We need to try to save the season and, at the moment, we'll just concentrate on playing for our Premier League life.
"The table is really tight and we are going to be doing our best to stay in the Premier League.
"We also need the fans' support because when you're on the pitch, under pressure and fighting for your life in the Premier League, you need encouragement."
West Brom, who have not won under Mel, visit Swansea City on Saturday.
