The Tigers must navigate a way past Tottenham in the fourth round of the competition first and City will be out for revenge after losing to a hotly-disputed penalty to the north Londoners at the weekend.
But Boyd remains adamant that although the club's main aim is to stay in the Premier League this campaign, there is no reason why they cannot challenge for honours in the League Cup too.
"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. And, in our case, the Capital One Cup probably represents our best chance of success," he told the Daily Star.
"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.
"Swansea showed what can be done by winning it last year. Hopefully, we can follow in their footsteps this season.
"We have got a fantastic opportunity and it is one we are determined to take.
"With a place in the Europa League on offer to the winners, it is a competition we are taking very seriously.
"This club has never competed in European competition and it would be great to be part of a Hull team which made that happen."