The Dutchman's arrival last August sparked an upturn in the northern club's fortunes after they had made one of the worst starts to a Bundesliga season in their history.
He only found the back of the net five times, however, as Hamburg's up-and-down season saw them miss out on a place in Europe.
And Van der Vaart would prefer there to be more ups than downs next season, starting with his own performances.
"I can understand everybody who is not happy with me because I'm not happy either," he told Bild.
"I need to play better and I would like to score more than 10 goals next season."
The 30-year-old was made Hamburg's captain during last season and coach Thorsten Fink hopes he will do more to repay the faith shown in him.
"As soon as he arrived, he had such an amazing impact on the whole club, spreading positive energy, but then he struggled after his injury break," Fink told Kicker magazine.
"Once he was made captain, he became stronger again. Overall, he really helped us, but I expect him to do even more in his second year."