The Merseyside outfit, who reached the semi-finals of the competition last term, have not won a trophy since lifting the FA Cup in 1995.
Speaking ahead of Saturday's third-round home clash with Leicester, Koeman said he would name a strong side for the tie, and added: "This competition is a title and if you ask every manager, they like to win titles.
"We know it is difficult, but we take it very seriously.
"We will go for it. We fight for everything this Saturday."