Karius committed two calamitous errors as Liverpool lost 3-1 to Real Madrid in Kiev on Saturday. The 24-year-old threw the ball directly into the leg of Karim Benzema to concede the opener, before allowing a long-range Gareth Bale strike to bounce off his gloves and into the back of the net.
The shot-stopper's future at Anfield is now reportedly in doubt, while police in Merseyside are investigating death threats made against him.
During a media conference in Germany's training camp, the national team's goalkeeping coach expressed his sympathy for the ordeal endured by Karius in recent days.
"What he went through was brutal," the 1990 World Cup and Euro 1996 winner said.
"We sent him a message after the final. We'll have to see how he handles the situation."
Manuel Neuer, Marc-Andre ter Stegen, Bernd Leno and Kevin Trapp were the goalkeepers selected by Joachim Low in Germany's provisional squad ahead of the World Cup.
Kopke confirmed former Mainz player Karius, capped from Under-16 to Under-21 level but yet to make a senior appearance, had been under consideration.
"We watched him for a long time," the 56-year-old said.
"Things are looking good for the future. He was on our list, but not in the final group. We can only wish him the best with handling this situation."