A 3-0 home loss to Hertha Berlin on Saturday left Hamburg second bottom in the table and firmly in a relegation fight, despite only being two points from safety.
A group of supporters demonstrated outside the Imtech Arena following the game, with the club's players coming under attack for another lacklustre performance as they made their way to their cars.
Van der Vaart acknowledged results have been poor and revealed some members of the Hamburg squad were scared by the angry confrontation.
"Attacking players is not the point, not at all," he told Bild. "We players were afraid of the fans. This is particularly difficult for our younger players.
"I played bad, we all played badly. We are not doing this on purpose. We must try and reach a turning point on the pitch."
Hamburg face bottom side Eintracht Braunschweig in their next league match on Saturday, but first have to contend with Bayern Munich in the DFB Pokal on Wednesday.
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