Kostner has lifted the Wolves off the foot of the Bundesliga and three points clear of the bottom three and he is under no illusion that defeats will come along the way to safety.
However, his aim is to make sure there are more wins than losses and he believes they are finally heading in the right direction.
"We are now playing better football," he said at a press conference.
"We are combining more and are not just hoofing the ball forwards all the time.
"The results may not have been right in our last games, but if we learn the basics and fight passionately while being clinical in front of goal, then we will soon be safe."
They face a Hamburg side once again deprived of Rafael van der Vaart and Heung Min-son, but Kostner is reading nothing into those absences.
"To say that they are coming here with a weakened side would be our first mistake," he said.
"They showed that on Tuesday with their strong game. Nevertheless, we want to win."
Hamburg's 3-1 win over Schalke in midweek has lifted them back into a group of teams chasing the top six.
"We showed against Schalke that we had learnt from our last away game," said their coach Thorsten Fink.
"I hope that they can now do the same all over again in Wolfsburg."
In addition to Van der Vaart and Heung, Fink is also without the suspended Tolgay Arslan while Marcell Jansen is out with a shoulder injury.
Ivica Olic and Josue are the only doubts for Kostner.