Kane was withdrawn at half-time of the chastening home loss after suffering knocks to both ankles in the first half, but it was the one to his left one that seemed most damaging.
The England captain has a long history of suffering ligament damage to his joints, but the fact he was able to play on until half-time may provide some hope to Spurs that it may not be too serious.
Klopp was pleased to see his side return to their best.
“It was good. It was necessary, it was a good moment to show. We are still here, that is good to know,” he said.
“I am completely happy about the performance. They put a proper shift in. It was a brave performance against a counter attacking monster, which is what they are, it makes it even more special. It was really good.
“It was a good game, a deserved win. The boys played a really good game. We scored the first goal in the perfect moment. The boys made a proper fight of it and I am really happy about that and played good football.”
Klopp has conceded that he might be forced into the transfer market for a new defender following Matip’s injury, which followed another muscle injury for Fabinho.
He said: “We thought the whole time it’s about doing the right thing. I am not picky.
“We need to find the right player, we have players, not a lot in the defensive line, it is incredible what is happening there, really incredible.”