Simeone refused to shake Klopp's hand after the final whistle and stormed down the tunnel.
But Klopp insists they both got caught up in the heat of the moment after a thrilling contest in Madrid, which resulted in Liverpool winning 3-2.
"We don't like that but yes the situation is clear," said Klopp to reporters.
"I want to shake his hand. His reaction for sure, like mine, was not so cool.
"The next time we see each other we will shake hands definitely. It's nothing. He was obviously angry, not with me but with the game. There is nothing else."
The win means Liverpool are now five points clear of Atleti on top of Group B with three games remaining in the group stage.
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