"He can't carry the load alone," said the under-fire Fink, whose side have lost their opening two Bundesliga games without scoring and have been knocked out of the German Cup by third tier Karlsruher. "I know there's a lot of hype surrounding him but we have to share the responsibility.
"After an orderly first half, we lost the match because of individual mistakes. In your own penalty area, you have to get rid of the ball," Fink told reporters following Saturday's 2-0 defeat at Werder Bremen.
"If we stop making mistakes, then we can start winning games."
With Van der Vaart watching from the stands, Hamburg gave away two penalties, one converted by Aaron Hunt and one saved by Rene Adler. Nils Petersen scored Bremen's second goal after new Hamburg signing Petr Jiracek lost possession in his own half.
However, Fink defended the performance of the Czech international.
"Jiracek fought well in midfield... I think the new signings have strengthened the team."
Six-times German champions Hamburg, the only ever-present team in the Bundesliga's 50-season history, narrowly avoided relegation last season, ending a run of nine successive finishes in the top half of the table.
Fink is their fifth coach in the last two years.
Hamburg announced the signing of former Real Madrid and Tottenham midfielder Van der Vaart on Friday, bringing him back to the club he left four seasons ago.