He had to settle for a place on the bench during their final warm-up game against Valencia on Saturday, with new boy Jordan Henderson operating on the right in the first half.
And Kuyt knows the fight for places is tougher now that it has been for some time.
"I am very happy with the signings we have made this summer and it was good for them to have their first game at Anfield," Kuyt, who came off the bench to nab a late goal against the Spanish side, told liverpoolfc.tv.
"Everyone wants to play, but rivalry is something that in my opinion belongs to a club such as Liverpool. That's what should happen, you have to double up in every position.
"We want to progress and move forward and to do that you need more than 11 good players."