Hoffenheim spotted an object flying over their training base during their final session prior to Wednesday's clash and alerted it to the police.
The flying of drones over groups of people in Germany is prohibited, and it had been alleged that the drone was being used by a Werder scout.
Baumann did acknowledge Werder had someone in the area, though he insisted "anything that is illegal is unacceptable".
The club have now admitted Baumann, coach Florian Kohfeldt and analysts were behind the incident.
A statement on Werder's website read: "Werder Bremen briefly brought a drone into action last Tuesday during TSG Hoffenheim's training.
"This is the result of a conversation between Werder CEO Baumann, head coach Kohfeldt and employees of the analysis department."
Baumann took full responsibility for the use of the drone and apologised in a news conference on Friday.
"We discussed everything internally. I take responsibility for this," he said. "If the action in Hoffenheim led to a certain uncertainty on the training ground, then we would like to apologise for that.
"A drone was flown for a short period, but didn't fly over the pitch their team was training on. There was no threat. Everything has been resolved with Hoffenheim.
"We have done nothing illegal. That would go against our club principles. We apologise to Hoffenheim if the incident has unnerved them. This is all we have to say on the matter."