The Reds closed the gap on Tottenham, the current occupants of the final Europa League place, on Saturday with a comprehensive 5-0 victory over Birmingham.
Kenny Dalglish's side are now just three points adrift of Spurs with four games remaining.
Kuyt, though, has been quick to play down talk of European qualification, with there still much work to be done before the campaign comes to a close.
He told Sky Sports: "The most important thing for us is to focus on our own games.
"The next one is Newcastle at home and we have to make sure we get the three points.
"We still have Spurs at home, but if we want something we have to win our own games and take things one game at a time. If we do that I think we will get really close."
Terrific
Kuyt was among the goals against Birmingham on Saturday, helping to cover the loss of Andy Carroll, who was rested.
He added: "Unfortunately Andy wasn't ready for this game, hopefully he will be for the next one.
"It was good for the manager to see that he has more options. I thought the team were terrific today.
"Andy has already shown quality and hopefully he will be back soon and our team will get better."
Maxi Rodriguez's hat-trick stole the show against the Blues, but youngsters John Flanagan and Jack Robinson put in promising displays to enhance their blossoming reputations.
"It's unfortunate for the lads who are injured but the way the young lads are playing, Flanno and Robbo, it's terrific," said Kuyt.
"Jay Spearing is doing very well at the moment and Martin Kelly was unfortunate to get injured, because he has done well. It's good to see so many young lads coming through."
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