The Reds reached their first Wembley final since 1996 when they defeated Manchester City in the Carling Cup semi-finals on Wednesday night.
However, should Kuyt fail to lift a trophy this season, he would be the club's longest-serving player in 40 years to not win a piece of silverware.
"I have been here a while now and have played in a Champions League final and semi-final and in the Europa League semi-final and been second in the league," said the Dutchman, who moved to Anfield in 2006.
"Sometimes it is like that in football. You just have to make sure you give everything to reach what you want to reach - I know it is not enough to be second.
"We are all desperate to win a trophy - it has been a while for us - and that's the target. It's great to be in a final and now hopefully we can finish it off."
Liverpool take on Cardiff City in the Carling Cup final on Sunday, February 26.