"A supporter jumped over something, was chased by some security guys, slipped and kicked his ankle. Crazy," Klopp said after Adrian saved Tammy Abraham's penalty in the shootout win."
He added: "Apart from that it was a brilliant night for him."
The incident happened as the Liverpool players were huddled together celebrating the match-winning save.
A supporter, attempting to join the group, ran towards them, slipping as he was grabbed by a steward, and collided with several players.
Klopp said: "There's no doubt about how much we love our fans, there's no doubt about that at all, but if they all could stop doing that - that's the worst example we have so far heard about.
"We played against Manchester City and someone ran on the pitch then.
"At Norwich, there was someone as well.
"I don't know what you can do about it in the stadium but that means there is a lot of responsibility for the supporters as well. If the one person cannot hesitate or stop himself, then the people around should do it because it's not funny. It's crazy. You think 'wow, how can something like this happen?'"