Julian Draxler and Klaas-Jan Huntelaar’s first-half goals were enough to seal victory, though Robert Lewandowski did pull one back for the visitors in the second period.
“Congratulations to Schalke for a deserved victory, but for us it still feels unnecessary because we had some very good moments in our game after Schalke had taken the lead," he said.
"In the first half we played too defensively and made some tactical mistakes. We allowed chances which we should not have been allowing.
"Whenever we were determined, we were dangerous, but we did not take our chances. Schalke had a lot more shots on goal. The second half was really entertaining. When we were throwing our players forward, Schalke attacked with chances on the break.
"A draw would not have been undeserved, but it was not to be. Schalke used their good half to get two goals, but our good phase could only muster one. Therefore, we deserved to lose."
S04 head coach Jens Keller was delighted that his side were able to do the double over their Ruhr rivals, but lamented Huntelaar’s potentially long-term injury.
"In the first half, we played outstandingly and were able to make one or two more goals from the aggressive duels that we won," the former Stuttgart coach added. "We also played very good football.
"The first goal was huge for us early on. I am proud of how the team held against the [BVB] pressure and earned plenty of counterattacking opportunities. Huntelaar’s [injury] could be long [term]."
With a crucial Champions League last-16 second leg against Galatasaray coming up this week, Schalke will be hoping that the Netherlands striker's injury is not as bad as first feared.