Pepe Mel earned his first victory in charge as West Brom came from a goal down to beat fellow strugglers Swansea 2-1 on Saturday.
The result, sealed by Mulumbu's late winner, ended an eight-game winless run in the Premier League and moved the club three points clear of the relegation zone.
And Mulumbu reckons it has given Mel's charges a platform to build on after doubts were cast over their ability to survive in the top flight.
"The best way to reply is on the pitch," he told the Express and Star. "I hope the fans stay with us.
"We have to work hard as a team to stay up and on Saturday we saw a team fight to stay in the Premier League.
"The first half we were poor but in the second we were more aggressive, had the intention to get on the ball and scored two brilliant goals. I'm really confident (we can stay up)."
West Brom travel Hull City this weekend and have just four home games remaining.
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