The Reds are on course for their worst league finish since being relegated from the top flight in 1954, despite winning the League Cup and reaching the FA Cup final.
Kuyt said that even winning the FA Cup will not make up for the team's performance in the Premier League.
"Whatever happens between now and the end of the season, we will not be happy or satisfied with the position in the league," The Mirror quotes Kuyt as saying.
"We are playing for Liverpool Football Club, and when you do that you have to win every game. We have lost too many games and too many points in the league."
Kuyt joined Liverpool from Dutch side Feyenoord in 2006.