Hamburg could not a find a way through the Furth defence in the first leg of their Bundesliga relegation play-off at the Imtech Arena.
The result leaves Mirko Slomka's men facing a nervous second-leg clash at the Trolli Arena on Sunday as Hamburg look to preserve their top-flight status.
"They (Furth) started very well and we came into the game late, but we were better in the second half," Van der Vaart said.
"We still have a good chance of winning and we know we need to improve for Sunday.
"We're staying positive, though. A club as great as this belongs in the Bundesliga."
Van der Vaart and his colleagues will need to reverse their appalling away form if they are to succeed - only rock-bottom Eintracht Braunschweig picked up fewer points on the road than Hamburg's nine in the regular season.
