The victory - HSV's first of the season - lifted them out of the Bundesliga's bottom three and dispelled some of the storm clouds.
However, Fink has warned that those clouds could soon come back if they fail to build on Saturday's triumph over a side who have now lost all four of their games in the top flight.
"This is always the way in football," he told Sky television. "We all know that. Bayern Munich know that - they drew 1-1 during the week and now they've won the Super Cup.
"We have a good team, but the others want to be at the top too. Today, we played well because the team knew what the stakes were.
"We know internally what we have got to do. We have four points now and that's not very much, but at least we've got a win.
"That's very important for the self-confidence and for the atmosphere here, but we know things can turn again very quickly."
Hamburg travel to Borussia Dortmund in their next game in a fortnight's time, after the international break.