The 29-year-old rejoined the German side in the summer from Tottenham and believes he has not yet reached his own expectations since he came back to Bundesliga.
"I have a higher standard for myself and would like to meet it," Van der Vaart told Bild.
"I cannot and will not be satisfied with the performances that I have shown so far. I need to get better."
The Netherlands international is also calling on the rest of his team-mates to improve, beginning with Hamburg's clash against Freiburg this weekend.
"The team and I have to turn things up a notch," the former Tottenham and Real Madrid star added. "Ideally, we start doing so on Sunday evening against Freiburg."
Thorsten Fink’s side are currently ninth in Bundesliga having taken 13 points from 10 games.