Batshuayi was carried off on a stretcher towards the end of Dortmund's 2-0 loss to Ruhr rivals Schalke in the Bundesliga on Sunday.
And Stoger, while unwilling to offer a diagnosis for Batshuayi's apparent ankle injury, accepted it could be a serious blow for the forward, who was seen leaving the stadium on crutches and was reportedly taken to hospital.
"He is in great pain," Stoger said. "It looked like he could be out for a long time. I hope it's not that bad."
Second-half strikes from Yevhen Konoplyanka and Naldo earned bragging rights for Schalke, who moved four points clear in second place thanks to their first win over BVB since 2014.
Stoger left Mario Gotze on the bench until after Naldo's 82nd-minute thunderbolt secured all three points, preferring teenager Jadon Sancho to the Germany star in his second substitution.
"Mario is a talented player," Stoger added. "But I have to give another chance to the team from the Stuttgart game after the good performance [a 3-0 win].
"We also have many other young players who can come from the squad. That's just as true for Mario as it is for them.
"We did not have the attacking impact, which you need in such a derby. You do not have to be surprised if you leave the field as a deserved loser."
Domenico Tedesco continues to impress in his first season as a Bundesliga coach, the 32-year-old on track to lead Schalke back into the Champions League.
"I'm happy for the team and the fans," Tedesco said. "We wanted to bounce back from last weekend [losing to Hamburg] and we managed that. I have to praise each and everyone of the lads out there today.
"It's a privilege to stand in the Nordkurve. The whole team deserves to celebrate with them. I thought the fans were going to tear up the arena if I didn't go up there!"