Reds boss Dalglish left the 31-year-old on the bench for large periods of the season, but Kuyt feels he is good enough to start every week.
He told The Sun: "Under this manager I don't have the feeling any more that he will put me in the side every week.
"I'm under no illusion about playing every week. But I believe I am still good enough to play for Liverpool every week."
Kuyt seems certain to leave Anfield, though he is keen to remain with the Reds.
"Deep in my heart I'd love to stay at Liverpool," he said.
Last month, Kuyt was seen having talks with Feyenoord technical director Martin van Geel, sparking reports he would sign for the Rotterdam club.
However, although the player admits he considered a move back to his former club, he believes he still has much to offer a top European side.
"The fact I held talks with Feyenoord indicates I wanted to give it a serious chance," he told AD Sportwereld.
"But in many ways the gap is too great at this moment in time.
"If I returned to Holland, I would have to take an 80% cut in my Liverpool wages."