Ole Gunnar Solskjaer's side moved level on points with 17th-placed West Brom thanks to their victory at the Cardiff City Stadium, with nine points separating the bottom eight sides in the Premier League.
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"It's got the teams just above us looking behind themselves now," he told the club's official website.
"Hopefully we can use this win as a springboard to go into the next game and pick up a positive result to push on up the league.
"[Solskjaer] wanted us to go out and express ourselves and that's what we did. He wanted us to get out on the front foot, which as a team we did well, playing to earn the points available to us. Now we want to push on and build on that as players."
Cardiff face tough fixtures against Everton and Liverpool before taking on strugglers West Brom and Crystal Palace as they seek to avoid an immediate return to the Championship.
Mutch claims the squad are ignoring suggestions that their fate is sealed, preferring instead to focus on each game at a time.
"It's one win down and we now go into the next nine games, seeing where we can get to," he added.
"We believe in ourselves and want to kick on. For some of the outside media, they've been saying we're definitely down there, but we've remained positive.
"[We] all know that we've got to keep on pushing between now and the end of the season."