The 3-1 victory over Manchester United, in which the Holland international scored his first Reds hat-trick, was their third successive home win over their arch-rivals.
In results between the current top four and Liverpool the Merseysiders' record is second only to Sir Alex Ferguson's side.
They have secured 10 points from six matches against United, Arsenal, Manchester City and Chelsea, while the Old Trafford club have taken 13 from a possible 21, including matches against Liverpool.
The reason Kenny Dalglish's team are six points off of the Champions League places and 18 adrift of league leaders United is their woeful record against clubs currently below them.
keep winning
Defeats to Blackpool (twice), Everton, Stoke City, Newcastle United, Wolverhampton Wanderers, Blackburn Rovers and West Ham United have seriously damaged their campaign.
But in their remaining nine matches only three - Arsenal, City and Tottenham Hotspur (the latter two at home) - are against teams above them and Kuyt has called for an all-round improvement.
"We want to win every game, we want to go on a run," he said. "The aim for us is consistency. We have shown that we can compete with the best, but competing with the best is not enough to win things.
"We have beaten United, we have beaten Chelsea (twice) but we also want to beat the other teams as well. You need to win, with all respect, against the West Hams and the Wolves and the Blackpools.
"Everyone is working really hard every day to go forward, and hopefully we can show that West Ham (a 3-1 defeat) last week was a mistake and go on a run of winning games. That will be our motivation for the coming games.
"We all know getting into the top four will be really difficult, but Birmingham winning the Carling Cup means there will not be as many places in the Europa League for us to get, so we need to keep winning our games, and then we will see what happens."
