Peter Bosz's side suffered their third Bundesliga defeat in a row at Mercedes-Benz Arena on Friday, with Chadrac Akolo and Josip Brekalo scoring for the hosts either side of a Maximilian Philipp strike following a missed Schurrle penalty.
Schurrle, starting a league game for the first time this season in place of Pierre-Emerick Aubameyang, who was dropped for a breach of discipline, felt Dortmund responded well to the blow of Akolo's fifth-minute opener but should have done more with their first-half chances.
The former Chelsea man also called on his team-mates to improve their defensive organisation in order to stop other teams exploiting them on the break.
"I think we played a good game, especially in the first half after the almost own-goal," he said immediately after the match. "We came back strong, had good control and played some good football. But we need to score more goals.
"In the second half, we didn't dominate the game as we wanted. It went from in front of their goal to the other goal and, as Borussia Dortmund, you can't let the game happen like this. We have to dominate and work the ball. We can't give them so many good chances."
Dortmund lost Sokratis Papastathopoulos at half-time but Schurrle refused to blame Stuttgart's second goal on replacement Dan-Axel Zagadou, who failed to stop the run of Brekalo.
"Dan came in and played a really good game," he said. "But when you're as open as we are, and they play so many counter-attacks, it's difficult to win games."
Schurrle, however, sees it as a chance to show the Dortmund fans the team is prepared to fight to improve.
"It's a good opportunity. It's the most important game for our fans and you saw they were behind us but were very frustrated at the end and disappointed with us," he added.
"We need to go back, work on our shape, build some stamina and then go and play in the Champions League and the derby."