Atleti secured a 1-0 victory thanks to an early goal from Saul Niguez.
It was a raucous crowd in Madrid and Klopp knows Atleti will face a similar atmosphere on Merseyside.
On getting booked in the second-half, Klopp said:"It was too much. I am pretty sure, was it a throw-in for us before the first goal? That doesn't help to stay calm. All human beings make mistakes.
"Welcome to Anfield. It is not over yet."