Klopp, however, noted that they are both emotional managers, adding it would be a different case when next they see each other, adding that they will shake hands definitely.
An emotional Simeone had snubbed a full-time handshake with Klopp and instead decided to run down the tunnel, much to the bemusement of the Liverpool coach.
Liverpool were two goals ahead within 13 minutes, thanks to goals from Mohamed Salah and Naby Keita.
But the former Premier League champions were pegged back in the first half through an Antoine Griezmann double.
Salah added his second of the night from the spot after Mario Hermoso was adjudged to have pushed Diogo Jota in the box
Speaking after the match, Klopp said Simeone’s actions were not right, before attempting to play down the situation.
“The situation is clear, I wanted to shake his hand and he didn’t want to. His reaction was for sure not right and mine was not too good as well,” he told BT Sport.
“But we are both emotional so when we see each other next time we will shake hands definitely and it’s like nothing happened.
“He was obviously angry not with me, but with the game, the world and it’s nothing else.”
It’s not the first time the pair have been embroiled in controversy after Klopp questioned why Atletico had not played ‘proper football’ when the Spanish side knocked the then holders Liverpool out of the Champions League in 2020.
