The Baggies will take on League Two outfit Newport County tomorrow night for a place in the third round of the competition.
In the past Premier League clubs have used the tournament to field their fringe and youth players, but Jones has insisted that West Brom will take each of their opponents seriously.
"It is big for us. Some managers take it differently, swapping and changing players, but from the moment the gaffer walked through the door he said he wanted to win a cup," said the 26-year-old defender.
"That is our aim again this year. I am sure we will go out with a strong XI and see how far we can go. I am desperate for a good cup run. There are players in the dressing room who have won the cup and say how great it is. We want that as a group so we will go out on Tuesday with a team to win."
West Brom won the League Cup for the one and only time back in 1966.