The Bluebirds are expected to shuffle their team ahead of their trip to Accrington Stanley, but Mutch has insisted that the Welsh outfit are eager to do well in the competition.
The 21-year-old told Wales Online: "I was at Birmingham in the season that they won the League Cup and were relegated from the Premier League, but I firmly believe that we can do well in both competitions.
"Winning can only be good for the squad and every player will go out looking for a win at Accrington this evening. Our aim is to have a good, long cup run.
"Anybody can win the trophy and we'll give it everything that we've got."
Mutch has made 24 appearances for Cardiff since his move from St Andrew's.