Steve Bruce's men enjoyed a fine run to the FA Cup final last season, before succumbing to an extra-time defeat against Arsenal.
Hull's consolation prize was a spot in the UEFA Europa League and those European commitments ensured the club would not enter the League Cup until the third round, with their attempt to return to Wembley starting at West Brom on Wednesday.
With five Premier League teams guaranteed to exit the competition before round four, Hull captain Davies feels the club can go far in the competition, providing that is not at the expense of their place in the top-flight.
"We go into every competition and want to win every game," Davies told reporters ahead of the meeting with his former side at The Hawthorns.
"I don't know about the importance of it because our goal is still now to stay in the Premier League, no matter what.
"I don't care about what signings we've made and what players we have got now, we need to stay in this league and that's the be all and end all.
"But obviously if we can go down to West Brom and get a victory there and get through to the next round, looking at the amount of head to head Premier League games, it would look like a very good chance of progressing further and further."
Elsewhere, Bruce confirmed that Hull's on-loan Newcastle United forward Hatem Ben Arfa will make his full debut in the clash.
