Bremen became the first side to be beaten by Augsburg in the Bundesliga this season thanks to goals from Tobias Werner, Stephan Hain and Daniel Baier, and Schaaf admitted that the best side had won the contest.
"We were too passive and Augsburg were more committed to the tackles and always closer to the ball," he said.
"We were unable to free ourselves from them and disturb our opponents.
"Furthermore, we are committing too many mistakes in our build-up play and are not playing with enough assurance to cause our opponents problems.
"If you play like we did today [Friday], then you cannot win."
The victory provided a mixture of joy and relief for Augsburg coach Markus Weinzierl, himself celebrating his first ever win in the top flight of German football.
"We are relieved because we have been able to reward ourselves for our efforts," he said.
"We did not let their equaliser knock us down and we continued to play courageous, attacking football.
"In addition, we were well-organised in the defence and that was the key to the win."