Ole Gunnar Solskjaer's side have six games left to preserve their Premier League status and improve their current position sitting three points adrift in the bottom three
The Welsh outfit are three points from safety following Saturday's 3-3 draw with West Brom and are in danger of an immediate return to the Championship.
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"From now until the end of the season we need to look to get three points from every game," Mutch told BBC Sport.
"From 20th spot to 16th or 15th everyone is going to be looking to do that, and that isn't necessarily going to happen for every team.
"If we can pick up points over the next three games, we give ourselves a massive chance and put pressure [on] the teams around us."
Cardiff face fellow strugglers Crystal Palace on Saturday and have the prospect of a final-day home clash versus Chelsea to come.