The Austria international scored in the 5-0 win over Borussia Monchengladbach and Schaaf hopes to see more of the same now he has ended his drought.
"I think that Marko was pleased to have played such an eye-catching game," said Schaaf.
"But he also knows that he needs to keep repeating this performance and show it more often
"That is expected of him. It will be our job to achieve that with him.
"It is therefore a good thing when we can show him some positive things and I think that helps him too.
"We are hungry to experience more of it."
However, Arnautovic has warned that it is going to be harder for him to play a decisive role against Greuther Furth on Saturday.
"It is going to be a tough match," he said on his club's website. "It will be much harder than Augsburg.
"We are going to have to stay alert and take our chances effectively. But I hope I get to play another game like that one in Furth."
Arnautovic and co. can count on a warm welcome at the Furth Arena, not only because the Bavarians have yet to win at home all season.
Furth coach Mike Buskens was recently given a fair play award for his policy of shaking the hand of every member of the opposition when they take their places before the game.
"It is nothing extraordinary," he said. "I go to the visitors' bench before every game and greet them all.
"They may be our rivals, but they are also my guests. It's important to act respectfully with each other."
However, Buskens does not want to see any more niceties on the field from his team after eight games of the season.
"I hope that our settling in phase is now over," he said at a press conference.