"Really not good news, yes he will miss the World Cup," Klopp said. "Pretty serious injury in the calf muscle and now the process starts. That's it pretty much.
"All the rest will now follow in the next few days. Very sad news for the boy, for us as well and for Portugal... I don't want to put a time on it [his return]. It will be a long time."
Klopp added that Jota would not require surgery.
Jota, who has scored 10 times in 29 appearances for Portugal, had only regained full fitness after missing the opening few weeks of the season due to a hamstring problem.
Asked how Jota had taken the news, Klopp said: "He's surprisingly OK so far, a smart boy and he knew it when we carried him off. At that moment he knew it."
"After such a good night at Anfield mine ended in the worst way," Jota said in a statement on social media. "In the last minute one of my dreams collapsed.
"I will be one more supporting from the outside, club and country, and fighting to be back as soon as possible," he said, adding "You'll Never Walk Alone."
Klopp also rejected claims he had made xenophobic comments before the bad-tempered clash with City in the news conference on Wednesday.