The Royal Blues were eliminated from the competition on Wednesday after second-half goals from Patrice Covic and Christoph Daferner secured victory for the second-tier hosts. The result compounded concerns over Schalke's lack of goals and left Muslic demanding a response from his players.
“We are very disappointed and have to be very self-critical. The coming weeks will be very hard, but we will get through them,” Muslic said.
The coach was also unhappy with Hwang's behaviour during the match. The South Korean forward had to wait to return to the pitch while receiving treatment on the touchline and, in frustration, pushed one of Schalke's physiotherapists aside.
Muslic made clear that the incident would be addressed internally.
“I didn't like that. We will discuss it afterwards,” he said.
Hwang has endured a difficult start to the season since joining Schalke on loan from Wolverhampton Wanderers. The forward is still waiting for his first goal for the club, although he has recently been given opportunities to establish himself in the starting line-up.
He started against both Cologne and Dresden, but neither appearance produced the breakthrough he needs. His frustration against Dresden came during a match in which Schalke struggled to turn possession and attacking moves into clear chances.
Muslic nevertheless defended his forwards after the defeat, arguing that the team's problems cannot be attributed to individual strikers alone.
“I have to protect the strikers. It is a collective task for the team,” the coach said.
That assessment comes as Schalke consider strengthening their attack during the winter transfer window. Sporting director Frank Baumann is reportedly searching for affordable goalscorers who could improve the team's output without placing excessive pressure on the club's finances.
Schalke have struggled to score consistently in the league, and their cup elimination offered another example of an attack unable to convert promising situations into goals. The club are reported to be looking for additional firepower in January, with recruitment expected to focus particularly on the forward line.
The immediate challenge, however, is to restore confidence and improve results. Schalke face RB Leipzig on Saturday, giving Muslic little time to work on the team's shortcomings following the disappointment in Dresden.
The coach's message combines a demand for greater self-criticism with a defence of his attackers. He believes the forwards need better collective support, while Hwang must also respond to the frustration that overshadowed his performance.
With the league campaign continuing and the January window approaching, Schalke must address both their lack of goals and the discipline required to navigate a difficult period.