Goals from Marcos Reus and Sokratis Papastathopoulos in the opening 14 minutes had Jurgen Klopp's men in control at the SGL Arena on Friday.
Adrian Ramos made it 3-0 in the 78th minute, only for the visitors to endure a nervous finish as Augsburg pulled two goals back.
Subotic said his team deserved to be punished for the way they performed in the final 10 minutes.
"I'm happy that we won, but it was a close call in the end. We didn't really do that well as a team in the closing stages," he said.
"We stopped defending and Augsburg made the most of their chances. We all deserve a slap for those last 10 minutes."
It saw Dortmund bounce back from their 2-0 loss to Bayer Leverkusen in their Bundesliga opener.
Reus urged his team to learn from the mistakes they made late in the win over Augsburg, who had Raul Bobadilla and Tim Matavz net late.
"When I scored it was just pure joy. It's been a while since I've found the back of the net and of course we lost last week," he said.
"We reacted well though and played very well in the first half - we did exactly what our coach told us to.
"We lost focus in the second half and let Augsburg back into the game. We have to learn from those mistakes and do better next time."
Augsburg attacker Bobadilla lamented his side's first half, which proved costly in the end.
"I'm a bit disappointed. Dortmund were much better than us in the first half, but we gave everything in the second," the Argentine said.
"We scored two goals, but ultimately it wasn't enough."
