The Tigers travel to White Hart Lane for the second time in four days tonight to face Tottenham Hotspur in the fourth round of the competition.
Despite admitting that Premier League survival is the team's top priority, Boyd claims that cup success is also high on the agenda at the KC Stadium.
"Of course our biggest aim is to stay in the top flight, that's our priority, but we also want to try and do well in the cup competitions," he told the Daily Star.
"And, in our case, the League Cup probably represents our best chance of success. Obviously, recent seasons have suggested it is not as important to the bigger clubs, which means it's a competition that is up for grabs."
Hull were narrowly beaten 1-0 at Spurs in the Premier League on Sunday.