Manager fears Serbia's Filip Kostic sustained knee ligament damage
Kostic was forced off in the 43rd minute after a challenge with England midfielder Jude Bellingham which saw him fall to the ground and immediately ask for medical assistance.
The Juventus player walked off the pitch crying and was substituted by Filip Mladenovic.
"Kostic felt a strong pain in the outside part of his left knee and we fear that he could have ligament damage. He will undergo medical tests on Monday, let's hope it's not as bad as it looks," Stojkovic told a press conference at the Arena AufSchalke in Gelsenkirchen.
Stojkovic said that he believed his side should have snatched a better result in a feisty performance against England, mainly in the second half, after they rallied and forced a nervy end of encounter for their opponents.
"We managed to corner the English team and I think we didn't deserve to lose," Stojkovic said. "We were so close today against a quality opponent and I'm not satisfied by the result, not satisfied at all. But what can I do now?
"I told my players I was proud of their performance and about everything but the result. Now all we can do is to rest and get ready for what is ahead, probably the most important match of the group stage against Slovenia."
The result left Serbia bottom of Group C after Denmark and Slovenia drew 1-1 earlier on Sunday. England are top and play Denmark on Thursday when Serbia take on Slovenia.
